diff --git a/Lib/multiprocessing/shared_memory.py b/Lib/multiprocessing/shared_memory.py
index 99a8ce3320ad4e..80b4cf4c9038ef 100644
--- a/Lib/multiprocessing/shared_memory.py
+++ b/Lib/multiprocessing/shared_memory.py
@@ -74,12 +74,10 @@ class SharedMemory:
     _track = True
 
     def __init__(self, name=None, create=False, size=0, *, track=True):
-        if not size >= 0:
-            raise ValueError("'size' must be a positive integer")
+        if size < 0:
+            raise ValueError("'size' must be a non-negative integer")
         if create:
             self._flags = _O_CREX | os.O_RDWR
-            if size == 0:
-                raise ValueError("'size' must be a positive number different from zero")
         if name is None and not self._flags & os.O_EXCL:
             raise ValueError("'name' can only be None if create=True")
 
@@ -114,9 +112,11 @@ def __init__(self, name=None, create=False, size=0, *, track=True):
                     os.ftruncate(self._fd, size)
                 stats = os.fstat(self._fd)
                 size = stats.st_size
-                self._mmap = mmap.mmap(self._fd, size)
-            except OSError:
-                self.unlink()
+                if size > 0:
+                    self._mmap = mmap.mmap(self._fd, size)
+            except:
+                if create:
+                    _posixshmem.shm_unlink(self._name)
                 raise
             if self._track:
                 resource_tracker.register(self._name, "shared_memory")
@@ -125,7 +125,7 @@ def __init__(self, name=None, create=False, size=0, *, track=True):
 
             # Windows Named Shared Memory
 
-            if create:
+            if create and size > 0:
                 while True:
                     temp_name = _make_filename() if name is None else name
                     # Create and reserve shared memory block with this name
@@ -155,7 +155,9 @@ def __init__(self, name=None, create=False, size=0, *, track=True):
                         _winapi.CloseHandle(h_map)
                     self._name = temp_name
                     break
-
+            elif create and size == 0:
+                # TODO: Leave as None?
+                self._name = _make_filename() if name is None else name
             else:
                 self._name = name
                 # Dynamically determine the existing named shared memory
@@ -179,10 +181,14 @@ def __init__(self, name=None, create=False, size=0, *, track=True):
                     size = _winapi.VirtualQuerySize(p_buf)
                 finally:
                     _winapi.UnmapViewOfFile(p_buf)
-                self._mmap = mmap.mmap(-1, size, tagname=name)
+                if size > 0:
+                    self._mmap = mmap.mmap(-1, size, tagname=name)
 
         self._size = size
-        self._buf = memoryview(self._mmap)
+        if size > 0:
+            self._buf = memoryview(self._mmap)
+        else:
+            self._buf = memoryview(b'')
 
     def __del__(self):
         try:
diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index 4dc9a31d22f771..6514d0f786f6ea 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -4447,14 +4447,6 @@ def test_invalid_shared_memory_creation(self):
         with self.assertRaises(ValueError):
             sms_invalid = shared_memory.SharedMemory(create=True, size=-1)
 
-        # Test creating a shared memory segment with size 0
-        with self.assertRaises(ValueError):
-            sms_invalid = shared_memory.SharedMemory(create=True, size=0)
-
-        # Test creating a shared memory segment without size argument
-        with self.assertRaises(ValueError):
-            sms_invalid = shared_memory.SharedMemory(create=True)
-
     def test_shared_memory_pickle_unpickle(self):
         for proto in range(pickle.HIGHEST_PROTOCOL + 1):
             with self.subTest(proto=proto):
@@ -4851,6 +4843,33 @@ def test_shared_memory_tracking(self):
             resource_tracker.unregister(mem._name, "shared_memory")
             mem.close()
 
+    @unittest.skipIf(os.name != "posix", "windows automatically unlinks")
+    def test_creating_shm_unlinks_on_error(self):
+        name = self._new_shm_name("test_csuoe")
+        with unittest.mock.patch('mmap.mmap') as mock_mmap:
+            mock_mmap.side_effect = OSError("filesystems are evil")
+            with self.assertRaises(OSError):
+                shared_memory.SharedMemory(name, create=True, size=1)
+        with self.assertRaises(FileNotFoundError):
+            import _posixshmem
+            _posixshmem.shm_unlink(name)
+
+    def test_existing_shm_not_unlinked_on_error(self):
+        name = self._new_shm_name("test_esnuoe")
+        mem = shared_memory.SharedMemory(name, create=True, size=1)
+        self.addCleanup(mem.unlink)
+        with unittest.mock.patch('mmap.mmap') as mock_mmap:
+            mock_mmap.side_effect = OSError("filesystems are evil")
+            with self.assertRaises(OSError):
+                shared_memory.SharedMemory(name, create=False)
+
+    def test_zero_length_shared_memory(self):
+        name = self._new_shm_name("test_zlsm")
+        mem = shared_memory.SharedMemory(name, create=True, size=0)
+        self.addCleanup(mem.unlink)
+        self.assertEqual(mem.size, 0)
+        self.assertEqual(len(mem.buf), 0)
+
 #
 # Test to verify that `Finalize` works.
 #