diff --git a/openmc/bounding_box.py b/openmc/bounding_box.py
index 6e58ca8ba02..5f3d3a6cfdb 100644
--- a/openmc/bounding_box.py
+++ b/openmc/bounding_box.py
@@ -1,5 +1,5 @@
 from __future__ import annotations
-from typing import Iterable
+from collections.abc import Iterable
 
 import numpy as np
 
diff --git a/openmc/checkvalue.py b/openmc/checkvalue.py
index 42df3e5efbe..4fa205b14f7 100644
--- a/openmc/checkvalue.py
+++ b/openmc/checkvalue.py
@@ -1,12 +1,11 @@
 import copy
 import os
-import typing  # required to prevent typing.Union namespace overwriting Union
 from collections.abc import Iterable
 
 import numpy as np
 
 # Type for arguments that accept file paths
-PathLike = typing.Union[str, os.PathLike]
+PathLike = str | os.PathLike
 
 
 def check_type(name, value, expected_type, expected_iter_type=None, *, none_ok=False):
diff --git a/openmc/data/data.py b/openmc/data/data.py
index 7caf31e26ee..d94d6aaaa39 100644
--- a/openmc/data/data.py
+++ b/openmc/data/data.py
@@ -5,7 +5,6 @@
 from pathlib import Path
 from math import sqrt, log
 from warnings import warn
-from typing import Dict
 
 # Isotopic abundances from Meija J, Coplen T B, et al, "Isotopic compositions
 # of the elements 2013 (IUPAC Technical Report)", Pure. Appl. Chem. 88 (3),
@@ -283,13 +282,13 @@
 NEUTRON_MASS = 1.00866491595
 
 # Used in atomic_mass function as a cache
-_ATOMIC_MASS: Dict[str, float] = {}
+_ATOMIC_MASS: dict[str, float] = {}
 
 # Regex for GNDS nuclide names (used in zam function)
 _GNDS_NAME_RE = re.compile(r'([A-Zn][a-z]*)(\d+)((?:_[em]\d+)?)')
 
 # Used in half_life function as a cache
-_HALF_LIFE: Dict[str, float] = {}
+_HALF_LIFE: dict[str, float] = {}
 _LOG_TWO = log(2.0)
 
 def atomic_mass(isotope):
diff --git a/openmc/deplete/independent_operator.py b/openmc/deplete/independent_operator.py
index 250b94deb42..759abde1308 100644
--- a/openmc/deplete/independent_operator.py
+++ b/openmc/deplete/independent_operator.py
@@ -8,7 +8,6 @@
 from __future__ import annotations
 from collections.abc import Iterable
 import copy
-from typing import List, Set
 
 import numpy as np
 from uncertainties import ufloat
@@ -279,7 +278,7 @@ def _load_previous_results(self):
                 new_res = res_obj.distribute(self.local_mats, mat_indexes)
                 self.prev_res.append(new_res)
 
-    def _get_nuclides_with_data(self, cross_sections: List[MicroXS]) -> Set[str]:
+    def _get_nuclides_with_data(self, cross_sections: list[MicroXS]) -> set[str]:
         """Finds nuclides with cross section data"""
         return set(cross_sections[0].nuclides)
 
diff --git a/openmc/deplete/microxs.py b/openmc/deplete/microxs.py
index 253ba8c2a17..46ad2347e90 100644
--- a/openmc/deplete/microxs.py
+++ b/openmc/deplete/microxs.py
@@ -6,7 +6,7 @@
 
 from __future__ import annotations
 from tempfile import TemporaryDirectory
-from typing import List, Tuple, Iterable, Sequence
+from typing import Iterable, Sequence
 
 import pandas as pd
 import numpy as np
@@ -46,7 +46,7 @@ def get_microxs_and_flux(
         energies: Iterable[float] | str | None = None,
         chain_file: PathLike | None = None,
         run_kwargs=None
-    ) -> Tuple[List[np.ndarray], List[MicroXS]]:
+    ) -> tuple[list[np.ndarray], list[MicroXS]]:
     """Generate a microscopic cross sections and flux from a Model
 
     .. versionadded:: 0.14.0
@@ -183,7 +183,7 @@ class MicroXS:
         :data:`openmc.deplete.chain.REACTIONS`
 
     """
-    def __init__(self, data: np.ndarray, nuclides: List[str], reactions: List[str]):
+    def __init__(self, data: np.ndarray, nuclides: list[str], reactions: list[str]):
         # Validate inputs
         if data.shape[:2] != (len(nuclides), len(reactions)):
             raise ValueError(
diff --git a/openmc/deplete/openmc_operator.py b/openmc/deplete/openmc_operator.py
index 75f0925c4e7..c0ff568bc27 100644
--- a/openmc/deplete/openmc_operator.py
+++ b/openmc/deplete/openmc_operator.py
@@ -7,7 +7,6 @@
 
 from abc import abstractmethod
 from warnings import warn
-from typing import List, Tuple, Dict
 
 import numpy as np
 
@@ -185,7 +184,7 @@ def _differentiate_burnable_mats(self):
         """Assign distribmats for each burnable material"""
         pass
 
-    def _get_burnable_mats(self) -> Tuple[List[str], Dict[str, float], List[str]]:
+    def _get_burnable_mats(self) -> tuple[list[str], dict[str, float], list[str]]:
         """Determine depletable materials, volumes, and nuclides
 
         Returns
diff --git a/openmc/deplete/reaction_rates.py b/openmc/deplete/reaction_rates.py
index 4aaf829a9a5..714d9048b47 100644
--- a/openmc/deplete/reaction_rates.py
+++ b/openmc/deplete/reaction_rates.py
@@ -2,7 +2,6 @@
 
 An ndarray to store reaction rates with string, integer, or slice indexing.
 """
-from typing import Dict
 
 import numpy as np
 
@@ -53,9 +52,9 @@ class ReactionRates(np.ndarray):
     # the __array_finalize__ method (discussed here:
     # https://docs.scipy.org/doc/numpy/user/basics.subclassing.html)
 
-    index_mat: Dict[str, int]
-    index_nuc: Dict[str, int]
-    index_rx: Dict[str, int]
+    index_mat: dict[str, int]
+    index_nuc: dict[str, int]
+    index_rx: dict[str, int]
 
     def __new__(cls, local_mats, nuclides, reactions, from_results=False):
         # Create appropriately-sized zeroed-out ndarray
diff --git a/openmc/deplete/results.py b/openmc/deplete/results.py
index 7551379c64c..f897a88422c 100644
--- a/openmc/deplete/results.py
+++ b/openmc/deplete/results.py
@@ -1,8 +1,7 @@
 import numbers
 import bisect
 import math
-import typing  # required to prevent typing.Union namespace overwriting Union
-from typing import Iterable, Tuple, List
+from collections.abc import Iterable
 from warnings import warn
 
 import h5py
@@ -97,11 +96,11 @@ def from_hdf5(cls, filename: PathLike):
 
     def get_activity(
         self,
-        mat: typing.Union[Material, str],
+        mat: Material | str,
         units: str = "Bq/cm3",
         by_nuclide: bool = False,
         volume: float | None = None
-    ) -> Tuple[np.ndarray, typing.Union[np.ndarray, List[dict]]]:
+    ) -> tuple[np.ndarray, np.ndarray | list[dict]]:
         """Get activity of material over time.
 
         .. versionadded:: 0.14.0
@@ -152,11 +151,11 @@ def get_activity(
 
     def get_atoms(
         self,
-        mat: typing.Union[Material, str],
+        mat: Material | str,
         nuc: str,
         nuc_units: str = "atoms",
         time_units: str = "s"
-    ) -> Tuple[np.ndarray, np.ndarray]:
+    ) -> tuple[np.ndarray, np.ndarray]:
         """Get number of nuclides over time from a single material
 
         Parameters
@@ -215,11 +214,11 @@ def get_atoms(
 
     def get_decay_heat(
             self,
-            mat: typing.Union[Material, str],
+            mat: Material | str,
             units: str = "W",
             by_nuclide: bool = False,
             volume: float | None = None
-    ) -> Tuple[np.ndarray, typing.Union[np.ndarray, List[dict]]]:
+    ) -> tuple[np.ndarray, np.ndarray | list[dict]]:
         """Get decay heat of material over time.
 
         .. versionadded:: 0.14.0
@@ -242,7 +241,7 @@ def get_decay_heat(
         -------
         times : numpy.ndarray
             Array of times in [s]
-        decay_heat : numpy.ndarray or List[dict]
+        decay_heat : numpy.ndarray or list[dict]
             Array of total decay heat values if by_nuclide = False (default)
             or list of dictionaries of decay heat values by nuclide if
             by_nuclide = True.
@@ -270,11 +269,11 @@ def get_decay_heat(
         return times, decay_heat
 
     def get_mass(self,
-        mat: typing.Union[Material, str],
+        mat: Material | str,
         nuc: str,
         mass_units: str = "g",
         time_units: str = "s"
-    ) -> Tuple[np.ndarray, np.ndarray]:
+    ) -> tuple[np.ndarray, np.ndarray]:
         """Get mass of nuclides over time from a single material
 
         .. versionadded:: 0.14.0
@@ -324,10 +323,10 @@ def get_mass(self,
 
     def get_reaction_rate(
         self,
-        mat: typing.Union[Material, str],
+        mat: Material | str,
         nuc: str,
         rx: str
-    ) -> Tuple[np.ndarray, np.ndarray]:
+    ) -> tuple[np.ndarray, np.ndarray]:
         """Get reaction rate in a single material/nuclide over time
 
         Parameters
@@ -364,7 +363,7 @@ def get_reaction_rate(
 
         return times, rates
 
-    def get_keff(self, time_units: str = 's') -> Tuple[np.ndarray, np.ndarray]:
+    def get_keff(self, time_units: str = 's') -> tuple[np.ndarray, np.ndarray]:
         """Evaluates the eigenvalue from a results list.
 
         .. versionadded:: 0.13.1
@@ -400,7 +399,7 @@ def get_keff(self, time_units: str = 's') -> Tuple[np.ndarray, np.ndarray]:
         times = _get_time_as(times, time_units)
         return times, eigenvalues
 
-    def get_eigenvalue(self, time_units: str = 's') -> Tuple[np.ndarray, np.ndarray]:
+    def get_eigenvalue(self, time_units: str = 's') -> tuple[np.ndarray, np.ndarray]:
         warn("The get_eigenvalue(...) function has been renamed get_keff and "
              "will be removed in a future version of OpenMC.", FutureWarning)
         return self.get_keff(time_units)
diff --git a/openmc/geometry.py b/openmc/geometry.py
index f9b418ec1f7..6cce4c18c70 100644
--- a/openmc/geometry.py
+++ b/openmc/geometry.py
@@ -1,6 +1,5 @@
 from __future__ import annotations
 import os
-import typing
 from collections import defaultdict
 from copy import deepcopy
 from collections.abc import Iterable
@@ -41,7 +40,7 @@ class Geometry:
 
     def __init__(
         self,
-        root: openmc.UniverseBase | typing.Iterable[openmc.Cell] | None = None,
+        root: openmc.UniverseBase | Iterable[openmc.Cell] | None = None,
         merge_surfaces: bool = False,
         surface_precision: int = 10
     ):
@@ -316,7 +315,7 @@ def find(self, point) -> list:
         """
         return self.root_universe.find(point)
 
-    def get_instances(self, paths) -> typing.Union[int, typing.List[int]]:
+    def get_instances(self, paths) -> int | list[int]:
         """Return the instance number(s) for a cell/material in a geometry path.
 
         The instance numbers are used as indices into distributed
@@ -363,7 +362,7 @@ def get_instances(self, paths) -> typing.Union[int, typing.List[int]]:
 
         return indices if return_list else indices[0]
 
-    def get_all_cells(self) -> typing.Dict[int, openmc.Cell]:
+    def get_all_cells(self) -> dict[int, openmc.Cell]:
         """Return all cells in the geometry.
 
         Returns
@@ -377,7 +376,7 @@ def get_all_cells(self) -> typing.Dict[int, openmc.Cell]:
         else:
             return {}
 
-    def get_all_universes(self) -> typing.Dict[int, openmc.Universe]:
+    def get_all_universes(self) -> dict[int, openmc.Universe]:
         """Return all universes in the geometry.
 
         Returns
@@ -392,7 +391,7 @@ def get_all_universes(self) -> typing.Dict[int, openmc.Universe]:
         universes.update(self.root_universe.get_all_universes())
         return universes
 
-    def get_all_nuclides(self) -> typing.List[str]:
+    def get_all_nuclides(self) -> list[str]:
         """Return all nuclides within the geometry.
 
         Returns
@@ -406,7 +405,7 @@ def get_all_nuclides(self) -> typing.List[str]:
             all_nuclides |= set(material.get_nuclides())
         return sorted(all_nuclides)
 
-    def get_all_materials(self) -> typing.Dict[int, openmc.Material]:
+    def get_all_materials(self) -> dict[int, openmc.Material]:
         """Return all materials within the geometry.
 
         Returns
@@ -421,7 +420,7 @@ def get_all_materials(self) -> typing.Dict[int, openmc.Material]:
         else:
             return {}
 
-    def get_all_material_cells(self) -> typing.Dict[int, openmc.Cell]:
+    def get_all_material_cells(self) -> dict[int, openmc.Cell]:
         """Return all cells filled by a material
 
         Returns
@@ -440,7 +439,7 @@ def get_all_material_cells(self) -> typing.Dict[int, openmc.Cell]:
 
         return material_cells
 
-    def get_all_material_universes(self) -> typing.Dict[int, openmc.Universe]:
+    def get_all_material_universes(self) -> dict[int, openmc.Universe]:
         """Return all universes having at least one material-filled cell.
 
         This method can be used to find universes that have at least one cell
@@ -463,7 +462,7 @@ def get_all_material_universes(self) -> typing.Dict[int, openmc.Universe]:
 
         return material_universes
 
-    def get_all_lattices(self) -> typing.Dict[int, openmc.Lattice]:
+    def get_all_lattices(self) -> dict[int, openmc.Lattice]:
         """Return all lattices defined
 
         Returns
@@ -481,7 +480,7 @@ def get_all_lattices(self) -> typing.Dict[int, openmc.Lattice]:
 
         return lattices
 
-    def get_all_surfaces(self) -> typing.Dict[int, openmc.Surface]:
+    def get_all_surfaces(self) -> dict[int, openmc.Surface]:
         """
         Return all surfaces used in the geometry
 
@@ -517,7 +516,7 @@ def _get_domains_by_name(self, name, case_sensitive, matching, domain_type) -> l
 
     def get_materials_by_name(
         self, name, case_sensitive=False, matching=False
-    ) -> typing.List[openmc.Material]:
+    ) -> list[openmc.Material]:
         """Return a list of materials with matching names.
 
         Parameters
@@ -540,7 +539,7 @@ def get_materials_by_name(
 
     def get_cells_by_name(
         self, name, case_sensitive=False, matching=False
-    ) -> typing.List[openmc.Cell]:
+    ) -> list[openmc.Cell]:
         """Return a list of cells with matching names.
 
         Parameters
@@ -563,7 +562,7 @@ def get_cells_by_name(
 
     def get_surfaces_by_name(
         self, name, case_sensitive=False, matching=False
-    ) -> typing.List[openmc.Surface]:
+    ) -> list[openmc.Surface]:
         """Return a list of surfaces with matching names.
 
         .. versionadded:: 0.13.3
@@ -588,7 +587,7 @@ def get_surfaces_by_name(
 
     def get_cells_by_fill_name(
         self, name, case_sensitive=False, matching=False
-    ) -> typing.List[openmc.Cell]:
+    ) -> list[openmc.Cell]:
         """Return a list of cells with fills with matching names.
 
         Parameters
@@ -635,7 +634,7 @@ def get_cells_by_fill_name(
 
     def get_universes_by_name(
         self, name, case_sensitive=False, matching=False
-    ) -> typing.List[openmc.Universe]:
+    ) -> list[openmc.Universe]:
         """Return a list of universes with matching names.
 
         Parameters
@@ -658,7 +657,7 @@ def get_universes_by_name(
 
     def get_lattices_by_name(
         self, name, case_sensitive=False, matching=False
-    ) -> typing.List[openmc.Lattice]:
+    ) -> list[openmc.Lattice]:
         """Return a list of lattices with matching names.
 
         Parameters
@@ -679,7 +678,7 @@ def get_lattices_by_name(
         """
         return self._get_domains_by_name(name, case_sensitive, matching, 'lattice')
 
-    def remove_redundant_surfaces(self) -> typing.Dict[int, openmc.Surface]:
+    def remove_redundant_surfaces(self) -> dict[int, openmc.Surface]:
         """Remove and return all of the redundant surfaces.
 
         Uses surface_precision attribute of Geometry instance for rounding and
diff --git a/openmc/lib/mesh.py b/openmc/lib/mesh.py
index 519bf4770de..78566d449a6 100644
--- a/openmc/lib/mesh.py
+++ b/openmc/lib/mesh.py
@@ -1,8 +1,7 @@
-from collections.abc import Mapping
+from collections.abc import Mapping, Sequence
 from ctypes import (c_int, c_int32, c_char_p, c_double, POINTER, Structure,
                     create_string_buffer, c_uint64, c_size_t)
 from random import getrandbits
-from typing import List, Tuple, Sequence
 from weakref import WeakValueDictionary
 
 import numpy as np
@@ -171,7 +170,7 @@ def material_volumes(
             self,
             n_samples: int = 10_000,
             prn_seed: int | None = None
-    ) -> List[List[Tuple[Material, float]]]:
+    ) -> list[list[tuple[Material, float]]]:
         """Determine volume of materials in each mesh element
 
         .. versionadded:: 0.15.0
diff --git a/openmc/material.py b/openmc/material.py
index b1e3877db6a..2bbcc9fe43a 100644
--- a/openmc/material.py
+++ b/openmc/material.py
@@ -5,9 +5,7 @@
 from numbers import Real
 from pathlib import Path
 import re
-import typing  # imported separately as py3.8 requires typing.Iterable
 import warnings
-from typing import List, Dict
 
 import lxml.etree as ET
 import numpy as np
@@ -202,7 +200,7 @@ def depletable(self, depletable: bool):
         self._depletable = depletable
 
     @property
-    def paths(self) -> List[str]:
+    def paths(self) -> list[str]:
         if self._paths is None:
             raise ValueError('Material instance paths have not been determined. '
                              'Call the Geometry.determine_paths() method.')
@@ -217,15 +215,15 @@ def num_instances(self) -> int:
         return self._num_instances
 
     @property
-    def nuclides(self) -> List[namedtuple]:
+    def nuclides(self) -> list[namedtuple]:
         return self._nuclides
 
     @property
-    def isotropic(self) -> List[str]:
+    def isotropic(self) -> list[str]:
         return self._isotropic
 
     @isotropic.setter
-    def isotropic(self, isotropic: typing.Iterable[str]):
+    def isotropic(self, isotropic: Iterable[str]):
         cv.check_iterable_type('Isotropic scattering nuclides', isotropic,
                                str)
         self._isotropic = list(isotropic)
@@ -930,7 +928,7 @@ def add_s_alpha_beta(self, name: str, fraction: float = 1.0):
     def make_isotropic_in_lab(self):
         self.isotropic = [x.name for x in self._nuclides]
 
-    def get_elements(self) -> List[str]:
+    def get_elements(self) -> list[str]:
         """Returns all elements in the material
 
         .. versionadded:: 0.12
@@ -944,7 +942,7 @@ def get_elements(self) -> List[str]:
 
         return sorted({re.split(r'(\d+)', i)[0] for i in self.get_nuclides()})
 
-    def get_nuclides(self, element: str | None = None) -> List[str]:
+    def get_nuclides(self, element: str | None = None) -> list[str]:
         """Returns a list of all nuclides in the material, if the element
         argument is specified then just nuclides of that element are returned.
 
@@ -974,7 +972,7 @@ def get_nuclides(self, element: str | None = None) -> List[str]:
 
         return matching_nuclides
 
-    def get_nuclide_densities(self) -> Dict[str, tuple]:
+    def get_nuclide_densities(self) -> dict[str, tuple]:
         """Returns all nuclides in the material and their densities
 
         Returns
@@ -992,7 +990,7 @@ def get_nuclide_densities(self) -> Dict[str, tuple]:
 
         return nuclides
 
-    def get_nuclide_atom_densities(self, nuclide: str | None = None) -> Dict[str, float]:
+    def get_nuclide_atom_densities(self, nuclide: str | None = None) -> dict[str, float]:
         """Returns one or all nuclides in the material and their atomic
         densities in units of atom/b-cm
 
@@ -1078,7 +1076,7 @@ def get_nuclide_atom_densities(self, nuclide: str | None = None) -> Dict[str, fl
         return nuclides
 
     def get_activity(self, units: str = 'Bq/cm3', by_nuclide: bool = False,
-                     volume: float | None = None) -> Dict[str, float] | float:
+                     volume: float | None = None) -> dict[str, float] | float:
         """Returns the activity of the material or for each nuclide in the
         material in units of [Bq], [Bq/g] or [Bq/cm3].
 
@@ -1101,7 +1099,7 @@ def get_activity(self, units: str = 'Bq/cm3', by_nuclide: bool = False,
 
         Returns
         -------
-        typing.Union[dict, float]
+        Union[dict, float]
             If by_nuclide is True then a dictionary whose keys are nuclide
             names and values are activity is returned. Otherwise the activity
             of the material is returned as a float.
@@ -1125,7 +1123,7 @@ def get_activity(self, units: str = 'Bq/cm3', by_nuclide: bool = False,
         return activity if by_nuclide else sum(activity.values())
 
     def get_decay_heat(self, units: str = 'W', by_nuclide: bool = False,
-                       volume: float | None = None) -> Dict[str, float] | float:
+                       volume: float | None = None) -> dict[str, float] | float:
         """Returns the decay heat of the material or for each nuclide in the
         material in units of [W], [W/g] or [W/cm3].
 
@@ -1173,7 +1171,7 @@ def get_decay_heat(self, units: str = 'W', by_nuclide: bool = False,
 
         return decayheat if by_nuclide else sum(decayheat.values())
 
-    def get_nuclide_atoms(self, volume: float | None = None) -> Dict[str, float]:
+    def get_nuclide_atoms(self, volume: float | None = None) -> dict[str, float]:
         """Return number of atoms of each nuclide in the material
 
         .. versionadded:: 0.13.1
@@ -1311,8 +1309,8 @@ def _get_macroscopic_xml(self, macroscopic: str) -> ET.Element:
         return xml_element
 
     def _get_nuclides_xml(
-            self, nuclides: typing.Iterable[NuclideTuple],
-            nuclides_to_ignore: Iterable[str] | None = None)-> List[ET.Element]:
+            self, nuclides: Iterable[NuclideTuple],
+            nuclides_to_ignore: Iterable[str] | None = None)-> list[ET.Element]:
         xml_elements = []
 
         # Remove any nuclides to ignore from the XML export
@@ -1398,7 +1396,7 @@ def to_xml_element(
         return element
 
     @classmethod
-    def mix_materials(cls, materials, fracs: typing.Iterable[float],
+    def mix_materials(cls, materials, fracs: Iterable[float],
                       percent_type: str = 'ao', name: str | None = None) -> Material:
         """Mix materials together based on atom, weight, or volume fractions
 
diff --git a/openmc/mesh.py b/openmc/mesh.py
index 19555ae57c4..644f01fa72f 100644
--- a/openmc/mesh.py
+++ b/openmc/mesh.py
@@ -1,14 +1,12 @@
 from __future__ import annotations
-import typing
 import warnings
 from abc import ABC, abstractmethod
-from collections.abc import Iterable
+from collections.abc import Iterable, Sequence
 from functools import wraps
 from math import pi, sqrt, atan2
 from numbers import Integral, Real
 from pathlib import Path
 import tempfile
-from typing import Optional, Sequence, Tuple, List
 
 import h5py
 import lxml.etree as ET
@@ -154,7 +152,7 @@ def get_homogenized_materials(
             prn_seed: int | None = None,
             include_void: bool = True,
             **kwargs
-    ) -> List[openmc.Material]:
+    ) -> list[openmc.Material]:
         """Generate homogenized materials over each element in a mesh.
 
         .. versionadded:: 0.15.0
@@ -592,7 +590,7 @@ def _check_vtk_datasets(self, datasets: dict):
 
         """
         for label, dataset in datasets.items():
-            errmsg = (
+            errmsg = (ict
                 f"The size of the dataset '{label}' ({dataset.size}) should be"
                 f" equal to the number of mesh cells ({self.num_mesh_cells})"
             )
@@ -655,7 +653,7 @@ def dimension(self):
         return tuple(self._dimension)
 
     @dimension.setter
-    def dimension(self, dimension: typing.Iterable[int]):
+    def dimension(self, dimension: Iterable[int]):
         cv.check_type('mesh dimension', dimension, Iterable, Integral)
         cv.check_length('mesh dimension', dimension, 1, 3)
         self._dimension = dimension
@@ -672,7 +670,7 @@ def lower_left(self):
         return self._lower_left
 
     @lower_left.setter
-    def lower_left(self, lower_left: typing.Iterable[Real]):
+    def lower_left(self, lower_left: Iterable[Real]):
         cv.check_type('mesh lower_left', lower_left, Iterable, Real)
         cv.check_length('mesh lower_left', lower_left, 1, 3)
         self._lower_left = lower_left
@@ -692,7 +690,7 @@ def upper_right(self):
                 return [l + w * d for l, w, d in zip(ls, ws, dims)]
 
     @upper_right.setter
-    def upper_right(self, upper_right: typing.Iterable[Real]):
+    def upper_right(self, upper_right: Iterable[Real]):
         cv.check_type('mesh upper_right', upper_right, Iterable, Real)
         cv.check_length('mesh upper_right', upper_right, 1, 3)
         self._upper_right = upper_right
@@ -716,7 +714,7 @@ def width(self):
                 return [(u - l) / d for u, l, d in zip(us, ls, dims)]
 
     @width.setter
-    def width(self, width: typing.Iterable[Real]):
+    def width(self, width: Iterable[Real]):
         cv.check_type('mesh width', width, Iterable, Real)
         cv.check_length('mesh width', width, 1, 3)
         self._width = width
@@ -1484,7 +1482,7 @@ def __repr__(self):
     def get_indices_at_coords(
             self,
             coords: Sequence[float]
-        ) -> Tuple[int, int, int]:
+        ) -> tuple[int, int, int]:
         """Finds the index of the mesh voxel at the specified x,y,z coordinates.
 
         .. versionadded:: 0.15.0
@@ -1496,7 +1494,7 @@ def get_indices_at_coords(
 
         Returns
         -------
-        Tuple[int, int, int]
+        tuple[int, int, int]
             The r, phi, z indices
 
         """
@@ -1562,7 +1560,7 @@ def from_hdf5(cls, group: h5py.Group):
     @classmethod
     def from_domain(
         cls,
-        domain: typing.Union['openmc.Cell', 'openmc.Region', 'openmc.Universe', 'openmc.Geometry'],
+        domain: 'openmc.Cell' | 'openmc.Region' | 'openmc.Universe' | 'openmc.Geometry',
         dimension: Sequence[int] = (10, 10, 10),
         mesh_id: int | None = None,
         phi_grid_bounds: Sequence[float] = (0.0, 2*pi),
@@ -2215,7 +2213,7 @@ def volumes(self):
         return self._volumes
 
     @volumes.setter
-    def volumes(self, volumes: typing.Iterable[Real]):
+    def volumes(self, volumes: Iterable[Real]):
         cv.check_type("Unstructured mesh volumes", volumes, Iterable, Real)
         self._volumes = volumes
 
diff --git a/openmc/model/model.py b/openmc/model/model.py
index 2160c97e6cc..2ea579ab7df 100644
--- a/openmc/model/model.py
+++ b/openmc/model/model.py
@@ -6,7 +6,6 @@
 from numbers import Integral
 from tempfile import NamedTemporaryFile
 import warnings
-from typing import Optional, Dict
 
 import h5py
 import lxml.etree as ET
@@ -83,7 +82,7 @@ def __init__(self, geometry=None, materials=None, settings=None,
             self.plots = plots
 
     @property
-    def geometry(self) -> Optional[openmc.Geometry]:
+    def geometry(self) -> openmc.Geometry | None:
         return self._geometry
 
     @geometry.setter
@@ -92,7 +91,7 @@ def geometry(self, geometry):
         self._geometry = geometry
 
     @property
-    def materials(self) -> Optional[openmc.Materials]:
+    def materials(self) -> openmc.Materials | None:
         return self._materials
 
     @materials.setter
@@ -106,7 +105,7 @@ def materials(self, materials):
                 self._materials.append(mat)
 
     @property
-    def settings(self) -> Optional[openmc.Settings]:
+    def settings(self) -> openmc.Settings | None:
         return self._settings
 
     @settings.setter
@@ -115,7 +114,7 @@ def settings(self, settings):
         self._settings = settings
 
     @property
-    def tallies(self) -> Optional[openmc.Tallies]:
+    def tallies(self) -> openmc.Tallies | None:
         return self._tallies
 
     @tallies.setter
@@ -129,7 +128,7 @@ def tallies(self, tallies):
                 self._tallies.append(tally)
 
     @property
-    def plots(self) -> Optional[openmc.Plots]:
+    def plots(self) -> openmc.Plots | None:
         return self._plots
 
     @plots.setter
@@ -169,7 +168,7 @@ def _cells_by_id(self) -> dict:
 
     @property
     @lru_cache(maxsize=None)
-    def _cells_by_name(self) -> Dict[int, openmc.Cell]:
+    def _cells_by_name(self) -> dict[int, openmc.Cell]:
         # Get the names maps, but since names are not unique, store a set for
         # each name key. In this way when the user requests a change by a name,
         # the change will be applied to all of the same name.
@@ -182,7 +181,7 @@ def _cells_by_name(self) -> Dict[int, openmc.Cell]:
 
     @property
     @lru_cache(maxsize=None)
-    def _materials_by_name(self) -> Dict[int, openmc.Material]:
+    def _materials_by_name(self) -> dict[int, openmc.Material]:
         if self.materials is None:
             mats = self.geometry.get_all_materials().values()
         else:
diff --git a/openmc/model/surface_composite.py b/openmc/model/surface_composite.py
index 2945f73b71e..29411fe4608 100644
--- a/openmc/model/surface_composite.py
+++ b/openmc/model/surface_composite.py
@@ -1,12 +1,11 @@
 from abc import ABC, abstractmethod
-from collections.abc import Iterable
+from collections.abc import Iterable, Sequence
 from copy import copy
 from functools import partial
 from math import sqrt, pi, sin, cos, isclose
 from numbers import Real
 import warnings
 import operator
-from typing import Sequence
 
 import numpy as np
 from scipy.spatial import ConvexHull, Delaunay
diff --git a/openmc/plots.py b/openmc/plots.py
index 6a2b68332bd..7532d9d5cb1 100644
--- a/openmc/plots.py
+++ b/openmc/plots.py
@@ -1,7 +1,6 @@
 from collections.abc import Iterable, Mapping
 from numbers import Integral, Real
 from pathlib import Path
-from typing import Optional
 
 import h5py
 import lxml.etree as ET
diff --git a/openmc/settings.py b/openmc/settings.py
index 78821a3abd1..1f22347502f 100644
--- a/openmc/settings.py
+++ b/openmc/settings.py
@@ -4,7 +4,6 @@
 from math import ceil
 from numbers import Integral, Real
 from pathlib import Path
-import typing  # required to prevent typing.Union namespace overwriting Union
 
 import lxml.etree as ET
 
@@ -518,11 +517,11 @@ def max_order(self, max_order: int | None):
         self._max_order = max_order
 
     @property
-    def source(self) -> typing.List[SourceBase]:
+    def source(self) -> list[SourceBase]:
         return self._source
 
     @source.setter
-    def source(self, source: typing.Union[SourceBase, typing.Iterable[SourceBase]]):
+    def source(self, source: SourceBase | Iterable[SourceBase]):
         if not isinstance(source, MutableSequence):
             source = [source]
         self._source = cv.CheckedList(SourceBase, 'source distributions', source)
@@ -800,7 +799,7 @@ def temperature(self, temperature: dict):
         self._temperature = temperature
 
     @property
-    def trace(self) -> typing.Iterable:
+    def trace(self) -> Iterable:
         return self._trace
 
     @trace.setter
@@ -813,11 +812,11 @@ def trace(self, trace: Iterable):
         self._trace = trace
 
     @property
-    def track(self) -> typing.Iterable[typing.Iterable[int]]:
+    def track(self) -> Iterable[Iterable[int]]:
         return self._track
 
     @track.setter
-    def track(self, track: typing.Iterable[typing.Iterable[int]]):
+    def track(self, track: Iterable[Iterable[int]]):
         cv.check_type('track', track, Sequence)
         for t in track:
             if len(t) != 3:
@@ -900,12 +899,12 @@ def resonance_scattering(self, res: dict):
         self._resonance_scattering = res
 
     @property
-    def volume_calculations(self) -> typing.List[VolumeCalculation]:
+    def volume_calculations(self) -> list[VolumeCalculation]:
         return self._volume_calculations
 
     @volume_calculations.setter
     def volume_calculations(
-        self, vol_calcs: typing.Union[VolumeCalculation, typing.Iterable[VolumeCalculation]]
+        self, vol_calcs: VolumeCalculation | Iterable[VolumeCalculation]
     ):
         if not isinstance(vol_calcs, MutableSequence):
             vol_calcs = [vol_calcs]
@@ -999,11 +998,11 @@ def write_initial_source(self, value: bool):
         self._write_initial_source = value
 
     @property
-    def weight_windows(self) -> typing.List[WeightWindows]:
+    def weight_windows(self) -> list[WeightWindows]:
         return self._weight_windows
 
     @weight_windows.setter
-    def weight_windows(self, value: typing.Union[WeightWindows, typing.Iterable[WeightWindows]]):
+    def weight_windows(self, value: WeightWindows | Iterable[WeightWindows]):
         if not isinstance(value, MutableSequence):
             value = [value]
         self._weight_windows = cv.CheckedList(WeightWindows, 'weight windows', value)
@@ -1061,7 +1060,7 @@ def weight_windows_file(self, value: PathLike):
         self._weight_windows_file = value
 
     @property
-    def weight_window_generators(self) -> typing.List[WeightWindowGenerator]:
+    def weight_window_generators(self) -> list[WeightWindowGenerator]:
         return self._weight_window_generators
 
     @weight_window_generators.setter
diff --git a/openmc/source.py b/openmc/source.py
index 21dc305f348..e35e62f5fca 100644
--- a/openmc/source.py
+++ b/openmc/source.py
@@ -1,12 +1,10 @@
 from __future__ import annotations
 from abc import ABC, abstractmethod
-from collections.abc import Iterable
+from collections.abc import Iterable, Sequence
 from enum import IntEnum
 from numbers import Real
 import warnings
-import typing  # imported separately as py3.8 requires typing.Iterable
-# also required to prevent typing.Union namespace overwriting Union
-from typing import Sequence, Dict, Any
+from typing import Any
 
 import lxml.etree as ET
 import numpy as np
@@ -58,7 +56,7 @@ class SourceBase(ABC):
     def __init__(
         self,
         strength: float | None = 1.0,
-        constraints: Dict[str, Any] | None = None
+        constraints: dict[str, Any] | None = None
     ):
         self.strength = strength
         self.constraints = constraints
@@ -75,11 +73,11 @@ def strength(self, strength):
         self._strength = strength
 
     @property
-    def constraints(self) -> Dict[str, Any]:
+    def constraints(self) -> dict[str, Any]:
         return self._constraints
 
     @constraints.setter
-    def constraints(self, constraints: Dict[str, Any] | None):
+    def constraints(self, constraints: dict[str, Any] | None):
         self._constraints = {}
         if constraints is None:
             return
@@ -200,7 +198,7 @@ def from_xml_element(cls, elem: ET.Element, meshes=None) -> SourceBase:
                 raise ValueError(f'Source type {source_type} is not recognized')
 
     @staticmethod
-    def _get_constraints(elem: ET.Element) -> Dict[str, Any]:
+    def _get_constraints(elem: ET.Element) -> dict[str, Any]:
         # Find element containing constraints
         constraints_elem = elem.find("constraints")
         elem = constraints_elem if constraints_elem is not None else elem
@@ -315,7 +313,7 @@ def __init__(
         strength: float = 1.0,
         particle: str = 'neutron',
         domains: Sequence[openmc.Cell | openmc.Material | openmc.Universe] | None = None,
-        constraints: Dict[str, Any] | None = None
+        constraints: dict[str, Any] | None = None
     ):
         if domains is not None:
             warnings.warn("The 'domains' arguments has been replaced by the "
@@ -528,7 +526,7 @@ def __init__(
             self,
             mesh: MeshBase,
             sources: Sequence[SourceBase],
-            constraints: Dict[str, Any] | None  = None,
+            constraints: dict[str, Any] | None  = None,
     ):
         super().__init__(strength=None, constraints=constraints)
         self.mesh = mesh
@@ -705,7 +703,7 @@ def __init__(
         library: str | None  = None,
         parameters: str | None = None,
         strength: float = 1.0,
-        constraints: Dict[str, Any] | None = None
+        constraints: dict[str, Any] | None = None
     ) -> None:
         super().__init__(strength=strength, constraints=constraints)
 
@@ -831,7 +829,7 @@ def __init__(
         self,
         path: PathLike | None = None,
         strength: float = 1.0,
-        constraints: Dict[str, Any] | None = None
+        constraints: dict[str, Any] | None = None
     ):
         super().__init__(strength=strength, constraints=constraints)
         self._path = None
@@ -966,8 +964,8 @@ class SourceParticle:
     """
     def __init__(
         self,
-        r: typing.Iterable[float] = (0., 0., 0.),
-        u: typing.Iterable[float] = (0., 0., 1.),
+        r: Iterable[float] = (0., 0., 0.),
+        u: Iterable[float] = (0., 0., 1.),
         E: float = 1.0e6,
         time: float = 0.0,
         wgt: float = 1.0,
@@ -1003,7 +1001,7 @@ def to_tuple(self) -> tuple:
 
 
 def write_source_file(
-    source_particles: typing.Iterable[SourceParticle],
+    source_particles: Iterable[SourceParticle],
     filename: PathLike, **kwargs
 ):
     """Write a source file using a collection of source particles
@@ -1046,7 +1044,7 @@ def write_source_file(
         fh.create_dataset('source_bank', data=arr, dtype=source_dtype)
 
 
-def read_source_file(filename: PathLike) -> typing.List[SourceParticle]:
+def read_source_file(filename: PathLike) -> list[SourceParticle]:
     """Read a source file and return a list of source particles.
 
     .. versionadded:: 0.15.0
diff --git a/openmc/stats/multivariate.py b/openmc/stats/multivariate.py
index ce9740ad212..06c65896f49 100644
--- a/openmc/stats/multivariate.py
+++ b/openmc/stats/multivariate.py
@@ -1,7 +1,6 @@
 from __future__ import annotations
-import typing
 from abc import ABC, abstractmethod
-from collections.abc import Iterable
+from collections.abc import Iterable, Sequence
 from math import cos, pi
 from numbers import Real
 from warnings import warn
@@ -9,6 +8,7 @@
 import lxml.etree as ET
 import numpy as np
 
+import openmc
 import openmc.checkvalue as cv
 from .._xml import get_text
 from ..mesh import MeshBase
@@ -212,7 +212,7 @@ class Monodirectional(UnitSphere):
 
     """
 
-    def __init__(self, reference_uvw: typing.Sequence[float] = [1., 0., 0.]):
+    def __init__(self, reference_uvw: Sequence[float] = [1., 0., 0.]):
         super().__init__(reference_uvw)
 
     def to_xml_element(self):
@@ -789,8 +789,8 @@ class Box(Spatial):
 
     def __init__(
         self,
-        lower_left: typing.Sequence[float],
-        upper_right: typing.Sequence[float],
+        lower_left: Sequence[float],
+        upper_right: Sequence[float],
         only_fissionable: bool = False
     ):
         self.lower_left = lower_left
@@ -889,7 +889,7 @@ class Point(Spatial):
 
     """
 
-    def __init__(self, xyz: typing.Sequence[float] = (0., 0., 0.)):
+    def __init__(self, xyz: Sequence[float] = (0., 0., 0.)):
         self.xyz = xyz
 
     @property
@@ -939,9 +939,9 @@ def from_xml_element(cls, elem: ET.Element):
 def spherical_uniform(
         r_outer: float,
         r_inner: float = 0.0,
-        thetas: typing.Sequence[float] = (0., pi),
-        phis: typing.Sequence[float] = (0., 2*pi),
-        origin: typing.Sequence[float] = (0., 0., 0.)
+        thetas: Sequence[float] = (0., pi),
+        phis: Sequence[float] = (0., 2*pi),
+        origin: Sequence[float] = (0., 0., 0.)
     ):
     """Return a uniform spatial distribution over a spherical shell.
 
diff --git a/openmc/stats/univariate.py b/openmc/stats/univariate.py
index edfe10af74d..2d93b1f1b5d 100644
--- a/openmc/stats/univariate.py
+++ b/openmc/stats/univariate.py
@@ -1,9 +1,8 @@
 from __future__ import annotations
 import math
-import typing
 from abc import ABC, abstractmethod
 from collections import defaultdict
-from collections.abc import Iterable
+from collections.abc import Iterable, Sequence
 from copy import deepcopy
 from numbers import Real
 from warnings import warn
@@ -210,8 +209,8 @@ def from_xml_element(cls, elem: ET.Element):
     @classmethod
     def merge(
         cls,
-        dists: typing.Sequence[Discrete],
-        probs: typing.Sequence[int]
+        dists: Sequence[Discrete],
+        probs: Sequence[int]
     ):
         """Merge multiple discrete distributions into a single distribution
 
@@ -859,8 +858,8 @@ class Tabular(Univariate):
 
     def __init__(
             self,
-            x: typing.Sequence[float],
-            p: typing.Sequence[float],
+            x: Sequence[float],
+            p: Sequence[float],
             interpolation: str = 'linear-linear',
             ignore_negative: bool = False
         ):
@@ -1100,7 +1099,7 @@ class Legendre(Univariate):
 
     """
 
-    def __init__(self, coefficients: typing.Sequence[float]):
+    def __init__(self, coefficients: Sequence[float]):
         self.coefficients = coefficients
         self._legendre_poly = None
 
@@ -1156,8 +1155,8 @@ class Mixture(Univariate):
 
     def __init__(
         self,
-        probability: typing.Sequence[float],
-        distribution: typing.Sequence[Univariate]
+        probability: Sequence[float],
+        distribution: Sequence[Univariate]
     ):
         self.probability = probability
         self.distribution = distribution
@@ -1319,8 +1318,8 @@ def clip(self, tolerance: float = 1e-6, inplace: bool = False) -> Mixture:
 
 
 def combine_distributions(
-    dists: typing.Sequence[Univariate],
-    probs: typing.Sequence[float]
+    dists: Sequence[Univariate],
+    probs: Sequence[float]
 ):
     """Combine distributions with specified probabilities
 
diff --git a/openmc/weight_windows.py b/openmc/weight_windows.py
index ef118b7ea94..2bd442dd6da 100644
--- a/openmc/weight_windows.py
+++ b/openmc/weight_windows.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 from numbers import Real, Integral
-from typing import Iterable, List, Dict, Sequence
+from collections.abc import Iterable, Sequence
 import warnings
 
 import lxml.etree as ET
@@ -353,7 +353,7 @@ def to_xml_element(self) -> ET.Element:
         return element
 
     @classmethod
-    def from_xml_element(cls, elem: ET.Element, meshes: Dict[int, MeshBase]) -> WeightWindows:
+    def from_xml_element(cls, elem: ET.Element, meshes: dict[int, MeshBase]) -> WeightWindows:
         """Generate weight window settings from an XML element
 
         Parameters
@@ -407,7 +407,7 @@ def from_xml_element(cls, elem: ET.Element, meshes: Dict[int, MeshBase]) -> Weig
         )
 
     @classmethod
-    def from_hdf5(cls, group: h5py.Group, meshes: Dict[int, MeshBase]) -> WeightWindows:
+    def from_hdf5(cls, group: h5py.Group, meshes: dict[int, MeshBase]) -> WeightWindows:
         """Create weight windows from HDF5 group
 
         Parameters
@@ -457,7 +457,7 @@ def from_hdf5(cls, group: h5py.Group, meshes: Dict[int, MeshBase]) -> WeightWind
         )
 
 
-def wwinp_to_wws(path: PathLike) -> List[WeightWindows]:
+def wwinp_to_wws(path: PathLike) -> list[WeightWindows]:
     """Create WeightWindows instances from a wwinp file
 
     .. versionadded:: 0.13.1