Index: Doc/library/tarfile.rst
===================================================================
--- Doc/library/tarfile.rst	(revision 88932)
+++ Doc/library/tarfile.rst	(working copy)
@@ -372,7 +372,11 @@
       :meth:`read`, :meth:`readline`, :meth:`readlines`, :meth:`seek`, :meth:`tell`,
       and :meth:`close`, and also supports iteration over its lines.
 
+   .. versionchanged:: 3.3
+      The file-like object provides a no-op `flush` method, so that it can
+      be wrapped using :class:`io.TextIOWrapper`.
 
+
 .. method:: TarFile.add(name, arcname=None, recursive=True, exclude=None, *, filter=None)
 
    Add the file *name* to the archive. *name* may be any type of file
Index: Lib/tarfile.py
===================================================================
--- Lib/tarfile.py	(revision 88932)
+++ Lib/tarfile.py	(working copy)
@@ -893,6 +893,9 @@
         self.buffer = b""
         self.fileobj.seek(self.position)
 
+    def flush(self):
+        pass
+
     def close(self):
         """Close the file object.
         """
Index: Lib/test/test_tarfile.py
===================================================================
--- Lib/test/test_tarfile.py	(revision 88932)
+++ Lib/test/test_tarfile.py	(working copy)
@@ -442,6 +442,17 @@
         self.assertTrue((len(data), md5sum(data)) == (tarinfo.size, md5_regtype),
                 "regular file extraction failed")
 
+    def test_fileobj_regular_file_textiowrapper(self):
+        tarinfo = self.tar.next() # get "regtype" (can't use getmember)
+        fobj = self.tar.extractfile(tarinfo)
+        with io.TextIOWrapper(fobj) as fobj_wrapped:
+            data = fobj_wrapped.read()
+            data_bytes = data.encode()
+            self.assertTrue((len(data_bytes), md5sum(data_bytes)) ==
+                            (tarinfo.size, md5_regtype),
+                            "regular file extraction using TextIOWrapper "
+                            "failed")
+
     def test_provoke_stream_error(self):
         tarinfos = self.tar.getmembers()
         f = self.tar.extractfile(tarinfos[0]) # read the first member