diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index bbba2b45e5f..d01a6680e40 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -26,6 +26,7 @@ import warnings
 import test.support
 import test.support.script_helper
 from test import support
+from test.support import hashlib_helper
 from test.support import socket_helper
 from test.support import threading_helper
 
@@ -2954,6 +2955,8 @@ class _TestRemoteManager(BaseTestCase):
         # Make queue finalizer run before the server is stopped
         del queue
 
+
+@hashlib_helper.requires_hashdigest('md5')
 class _TestManagerRestart(BaseTestCase):
 
     @classmethod
@@ -3438,6 +3441,7 @@ class _TestPoll(BaseTestCase):
 #
 
 @unittest.skipUnless(HAS_REDUCTION, "test needs multiprocessing.reduction")
+@hashlib_helper.requires_hashdigest('md5')
 class _TestPicklingConnections(BaseTestCase):
 
     ALLOWED_TYPES = ('processes',)
@@ -3740,6 +3744,7 @@ class _TestSharedCTypes(BaseTestCase):
 
 
 @unittest.skipUnless(HAS_SHMEM, "requires multiprocessing.shared_memory")
+@hashlib_helper.requires_hashdigest('md5')
 class _TestSharedMemory(BaseTestCase):
 
     ALLOWED_TYPES = ('processes',)
@@ -4415,6 +4420,7 @@ class TestInvalidHandle(unittest.TestCase):
 
 
 
+@hashlib_helper.requires_hashdigest('md5')
 class OtherTest(unittest.TestCase):
     # TODO: add more tests for deliver/answer challenge.
     def test_deliver_challenge_auth_failure(self):
@@ -4451,6 +4457,7 @@ class OtherTest(unittest.TestCase):
 def initializer(ns):
     ns.test += 1
 
+@hashlib_helper.requires_hashdigest('md5')
 class TestInitializers(unittest.TestCase):
     def setUp(self):
         self.mgr = multiprocessing.Manager()
@@ -5305,6 +5312,7 @@ class TestPoolNotLeakOnFailure(unittest.TestCase):
             any(process.is_alive() for process in forked_processes))
 
 
+@hashlib_helper.requires_hashdigest('md5')
 class TestSyncManagerTypes(unittest.TestCase):
     """Test all the types which can be shared between a parent and a
     child process by using a manager which acts as an intermediary
@@ -5699,6 +5707,8 @@ def install_tests_in_module_dict(remote_globs, start_method):
                 Mixin = local_globs[type_.capitalize() + 'Mixin']
                 class Temp(base, Mixin, unittest.TestCase):
                     pass
+                if type_ == 'manager':
+                    Temp = hashlib_helper.requires_hashdigest('md5')(Temp)
                 Temp.__name__ = Temp.__qualname__ = newname
                 Temp.__module__ = __module__
                 remote_globs[newname] = Temp
diff --git a/Lib/test/test_concurrent_futures.py b/Lib/test/test_concurrent_futures.py
index 3b74949a5f6..0ed75e6098a 100644
--- a/Lib/test/test_concurrent_futures.py
+++ b/Lib/test/test_concurrent_futures.py
@@ -6,6 +6,7 @@ support.import_module('_multiprocessing')
 # Skip tests if sem_open implementation is broken.
 support.import_module('multiprocessing.synchronize')
 
+from test.support import hashlib_helper
 from test.support.script_helper import assert_python_ok
 
 import contextlib
@@ -953,6 +954,7 @@ class ProcessPoolExecutorTest(ExecutorTest):
         self.assertIn('raise RuntimeError(123) # some comment',
                       f1.getvalue())
 
+    @hashlib_helper.requires_hashdigest('md5')
     def test_ressources_gced_in_workers(self):
         # Ensure that argument for a job are correctly gc-ed after the job
         # is finished
diff --git a/Misc/NEWS.d/next/Tests/2020-05-26-07-53-31.bpo-17258.X_IKTQ.rst b/Misc/NEWS.d/next/Tests/2020-05-26-07-53-31.bpo-17258.X_IKTQ.rst
new file mode 100644
index 00000000000..0a4b329b802
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2020-05-26-07-53-31.bpo-17258.X_IKTQ.rst
@@ -0,0 +1 @@
+Skip some :mod:`multiprocessing` tests when MD5 hash digest is blocked.