diff --git a/docker/errors.py b/docker/errors.py
index d03e10f69..8b2762abe 100644
--- a/docker/errors.py
+++ b/docker/errors.py
@@ -150,6 +150,19 @@ def __init__(self, container, exit_status, command, image, stderr):
         )
 
 
+class ContainerStartError(DockerException):
+    """
+    Represents a container that has failed to start.
+    """
+    def __init__(self, container, reason):
+        self.container = container
+        self.msg = reason
+
+        super().__init__(
+            f"Container '{container.short_id}' failed to start: {reason}"
+        )
+
+
 class StreamParseError(RuntimeError):
     def __init__(self, reason):
         self.msg = reason
diff --git a/docker/models/containers.py b/docker/models/containers.py
index 4795523a1..99d614b7d 100644
--- a/docker/models/containers.py
+++ b/docker/models/containers.py
@@ -5,7 +5,9 @@
 from ..api import APIClient
 from ..constants import DEFAULT_DATA_CHUNK_SIZE
 from ..errors import (
+    APIError,
     ContainerError,
+    ContainerStartError,
     DockerException,
     ImageNotFound,
     NotFound,
@@ -842,6 +844,8 @@ def run(self, image, command=None, stdout=True, stderr=False,
             :py:class:`docker.errors.ContainerError`
                 If the container exits with a non-zero exit code and
                 ``detach`` is ``False``.
+            :py:class:`docker.errors.ContainerStartError`
+                If the container fails to start.
             :py:class:`docker.errors.ImageNotFound`
                 If the specified image does not exist.
             :py:class:`docker.errors.APIError`
@@ -880,7 +884,17 @@ def run(self, image, command=None, stdout=True, stderr=False,
             container = self.create(image=image, command=command,
                                     detach=detach, **kwargs)
 
-        container.start()
+        try:
+            container.start()
+        except APIError as e:
+            if remove:
+                container.remove()
+
+            if e.explanation:
+                error = e.explanation
+            else:
+                error = e
+            raise ContainerStartError(container, error) from e
 
         if detach:
             return container
diff --git a/tests/integration/models_containers_test.py b/tests/integration/models_containers_test.py
index 476263ae2..478c1bd34 100644
--- a/tests/integration/models_containers_test.py
+++ b/tests/integration/models_containers_test.py
@@ -158,13 +158,13 @@ def test_run_with_networking_config_with_undeclared_network(self):
             ),
         }
 
-        with pytest.raises(docker.errors.APIError):
-            container = client.containers.run(
+        with pytest.raises(docker.errors.ContainerStartError) as err:
+            client.containers.run(
                 'alpine', 'echo hello world', network=net_name,
                 networking_config=networking_config,
                 detach=True
             )
-            self.tmp_containers.append(container.id)
+            self.tmp_containers.append(err.container.id)
 
     def test_run_with_networking_config_only_undeclared_network(self):
         net_name = random_name()