diff --git a/changes/2418-PrettyWood.md b/changes/2418-PrettyWood.md
new file mode 100644
index 0000000000..cceb189661
--- /dev/null
+++ b/changes/2418-PrettyWood.md
@@ -0,0 +1 @@
+fix `mypy` complaints on `Path` and `UUID` related custom types
diff --git a/pydantic/_hypothesis_plugin.py b/pydantic/_hypothesis_plugin.py
index 0da35558f0..588e537646 100644
--- a/pydantic/_hypothesis_plugin.py
+++ b/pydantic/_hypothesis_plugin.py
@@ -139,10 +139,10 @@ def add_luhn_digit(card_number: str) -> str:
 )
 
 # UUIDs
-st.register_type_strategy(pydantic.UUID1, st.uuids(version=1))  # type: ignore[arg-type]
-st.register_type_strategy(pydantic.UUID3, st.uuids(version=3))  # type: ignore[arg-type]
-st.register_type_strategy(pydantic.UUID4, st.uuids(version=4))  # type: ignore[arg-type]
-st.register_type_strategy(pydantic.UUID5, st.uuids(version=5))  # type: ignore[arg-type]
+st.register_type_strategy(pydantic.UUID1, st.uuids(version=1))
+st.register_type_strategy(pydantic.UUID3, st.uuids(version=3))
+st.register_type_strategy(pydantic.UUID4, st.uuids(version=4))
+st.register_type_strategy(pydantic.UUID5, st.uuids(version=5))
 
 # Secrets
 st.register_type_strategy(pydantic.SecretBytes, st.binary().map(pydantic.SecretBytes))
diff --git a/pydantic/types.py b/pydantic/types.py
index 06220f771a..2e4eb284e3 100644
--- a/pydantic/types.py
+++ b/pydantic/types.py
@@ -517,8 +517,6 @@ def conlist(item_type: Type[T], *, min_items: int = None, max_items: int = None)
 
 
 if TYPE_CHECKING:
-    # TODO: add `str` and support it thanks to the plugin
-    # PyObject = Union[str, Callable[..., Any]]
     PyObject = Callable[..., Any]
 else:
 
@@ -632,10 +630,10 @@ def condecimal(
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ UUID TYPES ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 if TYPE_CHECKING:
-    UUID1 = Union[UUID, str]
-    UUID3 = Union[UUID, str]
-    UUID4 = Union[UUID, str]
-    UUID5 = Union[UUID, str]
+    UUID1 = UUID
+    UUID3 = UUID
+    UUID4 = UUID
+    UUID5 = UUID
 else:
 
     class UUID1(UUID):
@@ -658,8 +656,8 @@ class UUID5(UUID1):
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ PATH TYPES ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 if TYPE_CHECKING:
-    FilePath = Union[Path, str]
-    DirectoryPath = Union[Path, str]
+    FilePath = Path
+    DirectoryPath = Path
 else:
 
     class FilePath(Path):
diff --git a/tests/mypy/modules/success.py b/tests/mypy/modules/success.py
index b90abdede1..4d8d0c1411 100644
--- a/tests/mypy/modules/success.py
+++ b/tests/mypy/modules/success.py
@@ -208,15 +208,29 @@ class PydanticTypes(BaseModel):
     # String
     my_strict_str: StrictStr = 'pika'
     # PyObject
-    # TODO: my_pyobject_str: PyObject = 'datetime.date'
+    my_pyobject_str: PyObject = 'datetime.date'  # type: ignore
     my_pyobject_callable: PyObject = date
     # UUID
     my_uuid1: UUID1 = UUID('a8098c1a-f86e-11da-bd1a-00112444be1e')
-    my_uuid1_str: UUID1 = 'a8098c1a-f86e-11da-bd1a-00112444be1e'
+    my_uuid1_str: UUID1 = 'a8098c1a-f86e-11da-bd1a-00112444be1e'  # type: ignore
     # Path
-    my_file_path: FilePath = Path('root') / 'myfile.txt'
-    my_file_path_str: FilePath = 'root/myfile.txt'
-    my_dir_path: DirectoryPath = Path('root') / 'mydir'
-    my_dir_path_str: DirectoryPath = 'root/mydir'
+    my_file_path: FilePath = Path(__file__)
+    my_file_path_str: FilePath = __file__  # type: ignore
+    my_dir_path: DirectoryPath = Path('.')
+    my_dir_path_str: DirectoryPath = '.'  # type: ignore
     # Json
     my_json: Json = '{"hello": "world"}'
+
+    class Config:
+        validate_all = True
+
+
+validated = PydanticTypes()
+validated.my_pyobject_str(2021, 1, 1)
+validated.my_pyobject_callable(2021, 1, 1)
+validated.my_uuid1.hex
+validated.my_uuid1_str.hex
+validated.my_file_path.absolute()
+validated.my_file_path_str.absolute()
+validated.my_dir_path.absolute()
+validated.my_dir_path_str.absolute()