diff --git a/swh/core/tarball.py b/swh/core/tarball.py
--- a/swh/core/tarball.py
+++ b/swh/core/tarball.py
@@ -166,6 +166,13 @@
             _unpack_zip(tarpath, dest)
         else:
             raise
+    except NotADirectoryError:
+        if format and "tar" in format:
+            # some old tarballs might fail to be unpacked by shutil.unpack_archive,
+            # fallback using the tar command as last resort
+            _unpack_tar(tarpath, dest)
+        else:
+            raise
 
     normalize_permissions(dest)
 
diff --git a/swh/core/tests/test_tarball.py b/swh/core/tests/test_tarball.py
--- a/swh/core/tests/test_tarball.py
+++ b/swh/core/tests/test_tarball.py
@@ -1,12 +1,14 @@
-# Copyright (C) 2019-2021  The Software Heritage developers
+# Copyright (C) 2019-2022  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 import hashlib
+import io
 import os
 import shutil
 import stat
+import tarfile
 
 import pytest
 
@@ -209,21 +211,38 @@
                 assert file.stat().st_mode == 0o100644
 
 
-def test_unpcompress_zip_imploded(tmp_path, datadir):
-    """Unpack a zip archive with compression type 6 (implode),
-    not supported by python zipfile module.
-
-    """
-    filename = "msk316src.zip"
-    zippath = os.path.join(datadir, "archives", filename)
-
-    assert os.path.exists(zippath)
+def uncompress_archive_test(archive_path, tmp_path):
+    assert os.path.exists(archive_path)
 
-    extract_dir = os.path.join(tmp_path, filename)
+    extract_dir = os.path.join(tmp_path, "unpack", os.path.basename(archive_path))
+    tarball.uncompress(archive_path, extract_dir)
+    assert len(os.listdir(extract_dir)) > 0
 
-    tarball.uncompress(zippath, extract_dir)
 
-    assert len(os.listdir(extract_dir)) > 0
+def test_uncompress_tar_fallback_when_unpack_archive_failed(tmp_path):
+    """shutil.unpack_archive can fail unpacking a tarball with missing
+    directory bit set on folder contained in it while the tar command
+    succeeds to perform the same task so check the fallback of using
+    tar command works for such edge case.
+    """
+    archive_path = os.path.join(tmp_path, "repro.tar.gz")
+    tf = tarfile.open(archive_path, "w:gz")
+    ti = tarfile.TarInfo("dir")
+    ti.mode = 0o777
+    ti.type = tarfile.DIRTYPE
+    tf.addfile(ti)
+    ti = tarfile.TarInfo("dir/file")
+    tf.addfile(ti, io.BytesIO(b"hello world"))
+    tf.close()
+    uncompress_archive_test(archive_path, tmp_path)
+
+
+def test_uncompress_zip_imploded(tmp_path, datadir):
+    """Unpack a zip archive with compression type 6 (implode),
+    not supported by python zipfile module.
+    """
+    archive_path = os.path.join(datadir, "archives", "msk316src.zip")
+    uncompress_archive_test(archive_path, tmp_path)
 
 
 def test_uncompress_upper_archive_extension(tmp_path, datadir):