diff --git a/django/test/testcases.py b/django/test/testcases.py
index bf035bd531..911a2d50ac 100644
--- a/django/test/testcases.py
+++ b/django/test/testcases.py
@@ -1,6 +1,7 @@
 import difflib
 import json
 import logging
+import pickle
 import posixpath
 import sys
 import threading
@@ -92,6 +93,18 @@ def to_list(value):
     return value
 
 
+def is_pickable(obj):
+    """
+    Returns true if the object can be dumped and loaded through the pickle
+    module.
+    """
+    try:
+        pickle.loads(pickle.dumps(obj))
+    except (AttributeError, TypeError):
+        return False
+    return True
+
+
 def assert_and_parse_html(self, html, user_msg, msg):
     try:
         dom = parse_html(html)
@@ -303,6 +316,23 @@ class SimpleTestCase(unittest.TestCase):
         """
         self._setup_and_call(result)
 
+    def __getstate__(self):
+        """
+        Make SimpleTestCase picklable for parallel tests using subtests.
+        """
+        state = super().__dict__
+        # _outcome and _subtest cannot be tested on picklability, since they
+        # contain the TestCase itself, leading to an infinite recursion.
+        if state["_outcome"]:
+            pickable_state = {"_outcome": None, "_subtest": None}
+            for key, value in state.items():
+                if key in pickable_state or not is_pickable(value):
+                    continue
+                pickable_state[key] = value
+            return pickable_state
+
+        return state
+
     def debug(self):
         """Perform the same as __call__(), without catching the exception."""
         debug_result = _DebugResult()
diff --git a/tests/test_runner/test_parallel.py b/tests/test_runner/test_parallel.py
index e83f53bf4e..8f7bfd5cf8 100644
--- a/tests/test_runner/test_parallel.py
+++ b/tests/test_runner/test_parallel.py
@@ -51,6 +51,13 @@ class SampleFailingSubtest(SimpleTestCase):
             with self.subTest(index=i):
                 self.assertEqual(i, 1)
 
+    # This method name doesn't begin with "test" to prevent test discovery
+    # from seeing it.
+    def pickle_error_test(self):
+        with self.subTest("TypeError: cannot pickle memoryview object"):
+            self.x = memoryview(b"")
+            self.fail("expected failure")
+
 
 class RemoteTestResultTest(SimpleTestCase):
     def _test_error_exc_info(self):
@@ -106,6 +113,16 @@ class RemoteTestResultTest(SimpleTestCase):
         with self.assertRaisesMessage(TypeError, msg):
             result._confirm_picklable(not_unpicklable_error)
 
+    def test_unpicklable_subtest(self):
+        result = RemoteTestResult()
+        subtest_test = SampleFailingSubtest(methodName="pickle_error_test")
+        subtest_test.run(result=result)
+
+        events = result.events
+        subtest_event = events[1]
+        assertion_error = subtest_event[3]
+        self.assertEqual(str(assertion_error[1]), "expected failure")
+
     @unittest.skipUnless(tblib is not None, "requires tblib to be installed")
     def test_add_failing_subtests(self):
         """
diff --git a/tests/test_utils/test_testcase.py b/tests/test_utils/test_testcase.py
index eb6ca80036..0f41f29a23 100644
--- a/tests/test_utils/test_testcase.py
+++ b/tests/test_utils/test_testcase.py
@@ -1,12 +1,20 @@
+import pickle
 from functools import wraps
 
 from django.db import IntegrityError, connections, transaction
 from django.test import TestCase, skipUnlessDBFeature
-from django.test.testcases import DatabaseOperationForbidden, TestData
+from django.test.testcases import DatabaseOperationForbidden, SimpleTestCase, TestData
 
 from .models import Car, Person, PossessedCar
 
 
+class TestSimpleTestCase(SimpleTestCase):
+    def test_is_picklable_with_non_picklable_properties(self):
+        """ParallelTestSuite requires that all TestCases are picklable."""
+        self.non_picklable = lambda: 0
+        self.assertEqual(self, pickle.loads(pickle.dumps(self)))
+
+
 class TestTestCase(TestCase):
     @skipUnlessDBFeature("can_defer_constraint_checks")
     @skipUnlessDBFeature("supports_foreign_keys")