diff --git a/tests/layer_tests/pytorch_tests/test_index_select.py b/tests/layer_tests/pytorch_tests/test_index_select.py
index 1c8c2c91eb331c..1ba5d6c569cd6d 100644
--- a/tests/layer_tests/pytorch_tests/test_index_select.py
+++ b/tests/layer_tests/pytorch_tests/test_index_select.py
@@ -41,6 +41,7 @@ def forward_out(self, x, indices, out):
     @pytest.mark.parametrize("out", [False, True])
     @pytest.mark.nightly
     @pytest.mark.precommit
+    @pytest.mark.precommit_fx_backend
     def test_index_select(self, dim, out, indices, ie_device, precision, ir_version):
         self._test(*self.create_model(dim, out), ie_device, precision, ir_version,
                    kwargs_to_prepare_input={"index": indices, "out": out, "dim": dim})
diff --git a/tests/layer_tests/pytorch_tests/test_isinf.py b/tests/layer_tests/pytorch_tests/test_isinf.py
new file mode 100644
index 00000000000000..70be61a5070d9f
--- /dev/null
+++ b/tests/layer_tests/pytorch_tests/test_isinf.py
@@ -0,0 +1,33 @@
+# Copyright (C) 2018-2023 Intel Corporation
+# SPDX-License-Identifier: Apache-2.0
+
+import numpy as np
+import pytest
+import torch
+
+from pytorch_layer_test_class import PytorchLayerTest
+
+
+@pytest.mark.parametrize('input_tensor', (torch.tensor([1, float('inf'), 2, float('-inf'), float('nan')])))
+class TestIsInf(PytorchLayerTest):
+
+    def _prepare_input(self):
+        input_tensor = self.input_tensor
+        return (input_tensor,)
+
+    def create_model(self):
+        class aten_isinf(torch.nn.Module):
+
+            def forward(self, input_tensor):
+                return torch.isinf(input_tensor)
+
+        ref_net = None
+
+        return aten_isinf(), ref_net, "aten::isinf"
+
+    @pytest.mark.nightly
+    @pytest.mark.precommit
+    @pytest.mark.precommit_fx_backend
+    def test_isinf(self, ie_device, precision, ir_version, input_tensor):
+        self.input_tensor = input_tensor
+        self._test(*self.create_model(), ie_device, precision, ir_version)
diff --git a/tests/layer_tests/pytorch_tests/test_isnan.py b/tests/layer_tests/pytorch_tests/test_isnan.py
new file mode 100644
index 00000000000000..b2b5325ba11107
--- /dev/null
+++ b/tests/layer_tests/pytorch_tests/test_isnan.py
@@ -0,0 +1,33 @@
+# Copyright (C) 2018-2023 Intel Corporation
+# SPDX-License-Identifier: Apache-2.0
+
+import numpy as np
+import pytest
+import torch
+
+from pytorch_layer_test_class import PytorchLayerTest
+
+
+@pytest.mark.parametrize('input_tensor', (torch.tensor([1, float('nan'), 2])))
+class TestIsNan(PytorchLayerTest):
+
+    def _prepare_input(self):
+        input_tensor = self.input_tensor
+        return (input_tensor,)
+
+    def create_model(self):
+        class aten_isnan(torch.nn.Module):
+
+            def forward(self, input_tensor):
+                return torch.isnan(input_tensor)
+
+        ref_net = None
+
+        return aten_isnan(), ref_net, "aten::isnan"
+
+    @pytest.mark.nightly
+    @pytest.mark.precommit
+    @pytest.mark.precommit_fx_backend
+    def test_isnan(self, ie_device, precision, ir_version, input_tensor):
+        self.input_tensor = input_tensor
+        self._test(*self.create_model(), ie_device, precision, ir_version)
diff --git a/tests/layer_tests/pytorch_tests/test_unary_ops.py b/tests/layer_tests/pytorch_tests/test_unary_ops.py
index f495e7ba3d272f..1bda4ba4ba2e49 100644
--- a/tests/layer_tests/pytorch_tests/test_unary_ops.py
+++ b/tests/layer_tests/pytorch_tests/test_unary_ops.py
@@ -71,6 +71,7 @@ def _prepare_input(self):
     @pytest.mark.nightly
     @pytest.mark.precommit
     @pytest.mark.precommit_torch_export
+    @pytest.mark.precommit_fx_backend
     @pytest.mark.parametrize("dtype", [torch.float32, torch.float64, torch.int8, torch.uint8, torch.int32, torch.int64])
     @pytest.mark.parametrize("op_type",
     [