diff --git a/Lib/distutils/archive_util.py b/Lib/distutils/archive_util.py
index 565a3117b4b5e1..478f8ed1671895 100644
--- a/Lib/distutils/archive_util.py
+++ b/Lib/distutils/archive_util.py
@@ -103,10 +103,25 @@ def _set_uid_gid(tarinfo):
             tarinfo.uname = owner
         return tarinfo
 
+    _filter = _set_uid_gid
+
+    # SOURCE_DATE EPOCH is defined there
+    # https://reproducible-builds.org/specs/source-date-epoch/
+    # we are at least sure that when it is set no timestamp can be later than
+    # this.
+    if (sde:= os.environ.get('SOURCE_DATE_EPOCH')):
+        timestamp = int(sde)
+
+        def _respect_SOURCE_DATE_EPOCH(tarinfo):
+            tarinfo.mtime = min(tarinfo.mtime, timestamp)
+            return tarinfo
+
+        _filter = lambda x: _respect_SOURCE_DATE_EPOCH(_set_uid_gid(x))
+
     if not dry_run:
         tar = tarfile.open(archive_name, 'w|%s' % tar_compression[compress])
         try:
-            tar.add(base_dir, filter=_set_uid_gid)
+            tar.add(base_dir, filter=_filter)
         finally:
             tar.close()
 
diff --git a/Lib/distutils/tests/test_archive_util.py b/Lib/distutils/tests/test_archive_util.py
index e9aad0e40fd14c..fbde589f5e7bfb 100644
--- a/Lib/distutils/tests/test_archive_util.py
+++ b/Lib/distutils/tests/test_archive_util.py
@@ -306,6 +306,24 @@ def test_make_archive_tar(self):
         self.assertEqual(os.path.basename(res), 'archive.tar')
         self.assertEqual(self._tarinfo(res), self._created_files)
 
+    def test_make_archive_tar_source_date_epoch(self):
+        ORIGINAL_SDE = os.environ.get('SOURCE_DATE_EPOCH')
+        try:
+            os.environ['SOURCE_DATE_EPOCH'] = '1337'
+            base_dir =  self._create_files()
+            base_name = os.path.join(self.mkdtemp() , 'archive')
+            res = make_archive(base_name, 'tar', base_dir, 'dist')
+
+            archive = tarfile.open(res,mode='r')
+            for item in archive:
+                self.assertLessEqual(item.mtime, 1337)
+        finally:
+            archive.close()
+            if ORIGINAL_SDE is None:
+                del os.environ['SOURCE_DATE_EPOCH']
+            else:
+                os.environ['SOURCE_DATE_EPOCH'] = ORIGINAL_SDE
+
     @unittest.skipUnless(ZLIB_SUPPORT, 'Need zlib support to run')
     def test_make_archive_gztar(self):
         base_dir =  self._create_files()
diff --git a/Misc/NEWS.d/next/Library/2020-05-23-12-05-15.bpo-38632.nFTEqW.rst b/Misc/NEWS.d/next/Library/2020-05-23-12-05-15.bpo-38632.nFTEqW.rst
new file mode 100644
index 00000000000000..828f7640e675af
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-05-23-12-05-15.bpo-38632.nFTEqW.rst
@@ -0,0 +1,5 @@
+Partial support for ``SOURCE_DATE_EPOCH`` environment variable for sdists
+has been added in distutils. When the ``SOURCE_DATE_EPOCH`` environment
+variable is set, the ``mtime`` of the files in an sdist tar archive will not
+be later than ``SOURCE_DATE_EPOCH``. This is a firs step to simplify getting
+byte identical reproducibility of source dists.