diff --git a/openapi_core/casting/schemas/casters.py b/openapi_core/casting/schemas/casters.py
index 6bbb3374..76737ab0 100644
--- a/openapi_core/casting/schemas/casters.py
+++ b/openapi_core/casting/schemas/casters.py
@@ -11,6 +11,8 @@
 
 from openapi_core.casting.schemas.exceptions import CastError
 from openapi_core.schema.schemas import get_properties
+from openapi_core.util import BOOLEAN_FALSE_VALUES
+from openapi_core.util import BOOLEAN_TRUE_VALUES
 from openapi_core.util import forcebool
 from openapi_core.validation.schemas.validators import SchemaValidator
 
@@ -65,7 +67,7 @@ def validate(self, value: Any) -> None:
         if isinstance(value, bool):
             return
 
-        if value.lower() not in ["false", "true"]:
+        if value.lower() not in BOOLEAN_TRUE_VALUES + BOOLEAN_FALSE_VALUES:
             raise ValueError("not a boolean format")
 
     def cast(self, value: Union[str, bytes]) -> bool:
diff --git a/openapi_core/util.py b/openapi_core/util.py
index d8c5da16..029b3602 100644
--- a/openapi_core/util.py
+++ b/openapi_core/util.py
@@ -4,13 +4,16 @@
 from typing import Any
 from typing import Iterable
 
+BOOLEAN_TRUE_VALUES = ("y", "yes", "t", "true", "on", "1")
+BOOLEAN_FALSE_VALUES = ("n", "no", "f", "false", "off", "0")
+
 
 def forcebool(val: Any) -> bool:
     if isinstance(val, str):
         val = val.lower()
-        if val in ("y", "yes", "t", "true", "on", "1"):
+        if val in BOOLEAN_TRUE_VALUES:
             return True
-        elif val in ("n", "no", "f", "false", "off", "0"):
+        elif val in BOOLEAN_FALSE_VALUES:
             return False
         else:
             raise ValueError(f"invalid truth value {val!r}")
diff --git a/tests/integration/data/v3.0/petstore.yaml b/tests/integration/data/v3.0/petstore.yaml
index 735fd96c..e0ea394f 100644
--- a/tests/integration/data/v3.0/petstore.yaml
+++ b/tests/integration/data/v3.0/petstore.yaml
@@ -286,6 +286,12 @@ paths:
       operationId: deleteTag
       tags:
         - tags
+      parameters:
+        - name: x-delete-force
+          in: header
+          schema:
+            type: boolean
+          required: false
       requestBody:
         required: false
         content:
diff --git a/tests/integration/test_petstore.py b/tests/integration/test_petstore.py
index fc59d3a8..11bfa250 100644
--- a/tests/integration/test_petstore.py
+++ b/tests/integration/test_petstore.py
@@ -2091,6 +2091,51 @@ def test_delete_tags_no_requestbody(self, spec):
 
         assert result.body is None
 
+    @pytest.mark.parametrize(
+        "header_value,expexted_value",
+        [
+            ("y", True),
+            ("t", True),
+            ("yes", True),
+            ("on", True),
+            ("true", True),
+            ("1", True),
+            ("n", False),
+            ("f", False),
+            ("no", False),
+            ("off", False),
+            ("false", False),
+            ("0", False),
+        ],
+    )
+    def test_delete_tags_header(self, spec, header_value, expexted_value):
+        host_url = "http://petstore.swagger.io/v1"
+        path_pattern = "/v1/tags"
+        headers = {
+            "x-delete-force": header_value,
+        }
+        request = MockRequest(
+            host_url,
+            "DELETE",
+            "/tags",
+            headers=headers,
+            path_pattern=path_pattern,
+        )
+
+        validate_request(request, spec=spec)
+
+        result = unmarshal_request(
+            request,
+            spec=spec,
+            cls=V30RequestParametersUnmarshaller,
+        )
+
+        assert result.parameters == Parameters(
+            header={
+                "x-delete-force": expexted_value,
+            },
+        )
+
     def test_delete_tags_raises_missing_required_response_header(
         self, spec, response_unmarshaller
     ):