diff --git a/Lib/shutil.py b/Lib/shutil.py
index a4ce2c0..223e9a8 100644
--- a/Lib/shutil.py
+++ b/Lib/shutil.py
@@ -53,6 +53,9 @@
 _USE_CP_SENDFILE = hasattr(os, "sendfile") and sys.platform.startswith("linux")
 _HAS_FCOPYFILE = posix and hasattr(posix, "_fcopyfile")  # macOS
 
+# CMD defaults in Windows 10
+_WIN_DEFAULT_PATHEXT = ".COM;.EXE;.BAT;.CMD;.VBS;.JS;.WS;.MSC"
+
 __all__ = ["copyfileobj", "copyfile", "copymode", "copystat", "copy", "copy2",
            "copytree", "move", "rmtree", "Error", "SpecialFileError",
            "ExecError", "make_archive", "get_archive_formats",
@@ -1415,7 +1418,9 @@
             path.insert(0, curdir)
 
         # PATHEXT is necessary to check on Windows.
-        pathext = os.environ.get("PATHEXT", "").split(os.pathsep)
+        pathext_source = os.getenv("PATHEXT") or _WIN_DEFAULT_PATHEXT
+        pathext = [ext for ext in pathext_source.split(os.pathsep) if ext]
+
         if use_bytes:
             pathext = [os.fsencode(ext) for ext in pathext]
         # See if the given file matches any of the expected path extensions.
diff --git a/Lib/test/test_shutil.py b/Lib/test/test_shutil.py
index e56b337..e19af64 100644
--- a/Lib/test/test_shutil.py
+++ b/Lib/test/test_shutil.py
@@ -1848,6 +1848,23 @@
             rv = shutil.which(program, path=self.temp_dir)
             self.assertEqual(rv, temp_filexyz.name)
 
+    # Issue 40592: See https://bugs.python.org/issue40592
+    @unittest.skipUnless(sys.platform == "win32", 'test specific to Windows')
+    def test_pathext_with_empty_str(self):
+        ext = ".xyz"
+        temp_filexyz = tempfile.NamedTemporaryFile(dir=self.temp_dir,
+                                                   prefix="Tmp2", suffix=ext)
+        self.addCleanup(temp_filexyz.close)
+
+        # strip path and extension
+        program = os.path.basename(temp_filexyz.name)
+        program = os.path.splitext(program)[0]
+
+        with support.EnvironmentVarGuard() as env:
+            env['PATHEXT'] = f"{ext};"  # note the ;
+            rv = shutil.which(program, path=self.temp_dir)
+            self.assertEqual(rv, temp_filexyz.name)
+
 
 class TestWhichBytes(TestWhich):
     def setUp(self):
diff --git a/Misc/NEWS.d/next/Library/2020-05-14-16-01-34.bpo-40592.Cmk855.rst b/Misc/NEWS.d/next/Library/2020-05-14-16-01-34.bpo-40592.Cmk855.rst
new file mode 100644
index 0000000..3211a1b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-05-14-16-01-34.bpo-40592.Cmk855.rst
@@ -0,0 +1 @@
+:func:`shutil.which` now ignores empty entries in :envvar:`PATHEXT` instead of treating them as a match.