diff --git a/pyproject.toml b/pyproject.toml
index da7590a..c3cff29 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -14,7 +14,7 @@ packages = [
 [tool.poetry.dependencies]
 python = "^3.7"
 tornado = "^4 || ^5 || ^6"
-openapi-core = "^0.13.4"
+openapi-core = "^0.13.8"
 ietfparse = "^1.7.0"
 typing-extensions = "^3.7.4"
 
diff --git a/tests/test_testing.py b/tests/test_testing.py
index cf0c6ce..846eb52 100644
--- a/tests/test_testing.py
+++ b/tests/test_testing.py
@@ -1,8 +1,9 @@
 import json
 
-from openapi_core.schema.responses.exceptions import InvalidResponse  # type: ignore
+from openapi_core.templating.responses.exceptions import (  # type: ignore
+    ResponseNotFound,
+)
 import tornado.web  # type: ignore
-
 from tornado_openapi3.handler import OpenAPIRequestHandler
 from tornado_openapi3.testing import AsyncOpenAPITestCase
 
@@ -102,7 +103,7 @@ class IncorrectResponseTests(BaseTestCase):
         handler.set_status(400)
 
     def test_unexpected_response_code(self) -> None:
-        with self.assertRaises(InvalidResponse) as context:
+        with self.assertRaises(ResponseNotFound) as context:
             self.fetch("/resource")
         self.assertEqual("400", context.exception.http_status)
 
diff --git a/tornado_openapi3/handler.py b/tornado_openapi3/handler.py
index fefc856..e0f87eb 100644
--- a/tornado_openapi3/handler.py
+++ b/tornado_openapi3/handler.py
@@ -7,15 +7,15 @@ from openapi_core.casting.schemas.exceptions import CastError  # type: ignore
 from openapi_core.exceptions import OpenAPIError  # type: ignore
 from openapi_core.deserializing.exceptions import DeserializeError  # type: ignore
 from openapi_core.schema.specs.models import Spec  # type: ignore
-from openapi_core.schema.media_types.exceptions import (  # type: ignore
-    InvalidContentType,
-)
 from openapi_core.schema.parameters.exceptions import (  # type: ignore
     MissingRequiredParameter,
 )
 from openapi_core.schema.request_bodies.exceptions import (  # type: ignore
     MissingRequestBody,
 )
+from openapi_core.templating.media_types.exceptions import (  # type: ignore
+    MediaTypeNotFound,
+)
 from openapi_core.templating.paths.exceptions import (  # type: ignore
     OperationNotFound,
     PathNotFound,
@@ -115,7 +115,7 @@ class OpenAPIRequestHandler(tornado.web.RequestHandler):
         |``InvalidSecurity``          |``401``   |Required authorization was missing   |
         |                             |          |from the request.                    |
         +-----------------------------+----------+-------------------------------------+
-        |``InvalidContentType``       |``415``   |The content type of the request did  |
+        |``MediaTypeNotFound``        |``415``   |The content type of the request did  |
         |                             |          |not match any of the types in the    |
         |                             |          |OpenAPI specification.               |
         +-----------------------------+----------+-------------------------------------+
@@ -152,7 +152,7 @@ class OpenAPIRequestHandler(tornado.web.RequestHandler):
             self.on_openapi_error(400, e)
         except InvalidSecurity as e:
             self.on_openapi_error(401, e)
-        except InvalidContentType as e:
+        except MediaTypeNotFound as e:
             self.on_openapi_error(415, e)
         except OpenAPIError as e:
             logger.exception("Unexpected validation failure")