diff --git a/config/default.yml b/config/default.yml
index 35e50559..e0dc4658 100644
--- a/config/default.yml
+++ b/config/default.yml
@@ -89,6 +89,11 @@ Sorbet/ForbidIncludeConstLiteral:
   VersionAdded: 0.2.0
   VersionChanged: 0.5.0
 
+Sorbet/ForbidTypeAliasedShapes:
+  Description: 'Forbids defining type aliases that contain shapes'
+  Enabled: false
+  VersionAdded: 0.7.6
+
 Sorbet/ForbidSuperclassConstLiteral:
   Description: 'Forbid superclasses which are non-literal constants.'
   Enabled: false
diff --git a/lib/rubocop/cop/sorbet/forbid_type_aliased_shapes.rb b/lib/rubocop/cop/sorbet/forbid_type_aliased_shapes.rb
new file mode 100644
index 00000000..51383d00
--- /dev/null
+++ b/lib/rubocop/cop/sorbet/forbid_type_aliased_shapes.rb
@@ -0,0 +1,44 @@
+# frozen_string_literal: true
+
+require "rubocop"
+
+module RuboCop
+  module Cop
+    module Sorbet
+      # Disallows defining type aliases that contain shapes
+      #
+      # @example
+      #
+      #  # bad
+      #  Foo = T.type_alias { { foo: Integer } }
+      #
+      #  # good
+      #  class Foo
+      #    extend T::Sig
+      #
+      #    sig { params(foo: Integer).void }
+      #    def initialize(foo)
+      #      @foo = foo
+      #    end
+      #  end
+      class ForbidTypeAliasedShapes < RuboCop::Cop::Base
+        MSG = "Type aliases shouldn't contain shapes because of significant performance overhead"
+
+        # @!method shape_type_alias?(node)
+        def_node_matcher(:shape_type_alias?, <<-PATTERN)
+          (block
+            (send (const {nil? cbase} :T) :type_alias)
+            (args)
+            `hash
+          )
+        PATTERN
+
+        def on_block(node)
+          add_offense(node) if shape_type_alias?(node)
+        end
+
+        alias_method :on_numblock, :on_block
+      end
+    end
+  end
+end
diff --git a/lib/rubocop/cop/sorbet_cops.rb b/lib/rubocop/cop/sorbet_cops.rb
index c22a3d14..4eb3dfee 100644
--- a/lib/rubocop/cop/sorbet_cops.rb
+++ b/lib/rubocop/cop/sorbet_cops.rb
@@ -7,6 +7,7 @@
 require_relative "sorbet/constants_from_strings"
 require_relative "sorbet/forbid_superclass_const_literal"
 require_relative "sorbet/forbid_include_const_literal"
+require_relative "sorbet/forbid_type_aliased_shapes"
 require_relative "sorbet/forbid_untyped_struct_props"
 require_relative "sorbet/implicit_conversion_method"
 require_relative "sorbet/one_ancestor_per_line"
diff --git a/manual/cops.md b/manual/cops.md
index 40704880..33e996b9 100644
--- a/manual/cops.md
+++ b/manual/cops.md
@@ -23,6 +23,7 @@ In the following section you find all available cops:
 * [Sorbet/ForbidTStruct](cops_sorbet.md#sorbetforbidtstruct)
 * [Sorbet/ForbidTUnsafe](cops_sorbet.md#sorbetforbidtunsafe)
 * [Sorbet/ForbidTUntyped](cops_sorbet.md#sorbetforbidtuntyped)
+* [Sorbet/ForbidTypeAliasedShapes](cops_sorbet.md#sorbetforbidtypealiasedshapes)
 * [Sorbet/ForbidUntypedStructProps](cops_sorbet.md#sorbetforbiduntypedstructprops)
 * [Sorbet/HasSigil](cops_sorbet.md#sorbethassigil)
 * [Sorbet/IgnoreSigil](cops_sorbet.md#sorbetignoresigil)
diff --git a/manual/cops_sorbet.md b/manual/cops_sorbet.md
index 4989af05..07fa9ab6 100644
--- a/manual/cops_sorbet.md
+++ b/manual/cops_sorbet.md
@@ -496,6 +496,31 @@ sig { params(my_argument: String).void }
 def foo(my_argument); end
 ```
 
+## Sorbet/ForbidTypeAliasedShapes
+
+Enabled by default | Safe | Supports autocorrection | VersionAdded | VersionChanged
+--- | --- | --- | --- | ---
+Disabled | Yes | No | 0.7.6 | -
+
+Disallows defining type aliases that contain shapes
+
+### Examples
+
+```ruby
+# bad
+Foo = T.type_alias { { foo: Integer } }
+
+# good
+class Foo
+  extend T::Sig
+
+  sig { params(foo: Integer).void }
+  def initialize(foo)
+    @foo = foo
+  end
+end
+```
+
 ## Sorbet/ForbidUntypedStructProps
 
 Enabled by default | Safe | Supports autocorrection | VersionAdded | VersionChanged
diff --git a/spec/rubocop/cop/sorbet/forbid_type_aliased_shapes_spec.rb b/spec/rubocop/cop/sorbet/forbid_type_aliased_shapes_spec.rb
new file mode 100644
index 00000000..09508971
--- /dev/null
+++ b/spec/rubocop/cop/sorbet/forbid_type_aliased_shapes_spec.rb
@@ -0,0 +1,35 @@
+# frozen_string_literal: true
+
+require "spec_helper"
+
+RSpec.describe(RuboCop::Cop::Sorbet::ForbidTypeAliasedShapes, :config) do
+  def message
+    "Type aliases shouldn't contain shapes because of significant performance overhead"
+  end
+
+  it("allows defining type aliases that don't contain shapes") do
+    expect_no_offenses(<<~RUBY)
+      Foo = T.type_alias { Integer }
+    RUBY
+  end
+
+  it("disallows defining type aliases that contain shapes") do
+    expect_offense(<<~RUBY)
+      Foo = T.type_alias { { foo: Integer } }
+            ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ #{message}
+    RUBY
+  end
+
+  it("disallows defining type aliases that contain nested shapes") do
+    expect_offense(<<~RUBY)
+      A = T.type_alias { [{ foo: Integer }] }
+          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ #{message}
+      B = T.type_alias { T.nilable({ foo: Integer }) }
+          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ #{message}
+      C = T.type_alias { T::Hash[Symbol, { foo: Integer }] }
+          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ #{message}
+      D = T.type_alias { T::Hash[Symbol, T::Array[T.any(String, { foo: Integer })]] }
+          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ #{message}
+    RUBY
+  end
+end