diff --git a/Lib/multiprocessing/shared_memory.py b/Lib/multiprocessing/shared_memory.py
index 184e36704baaeb..f92eb012c83160 100644
--- a/Lib/multiprocessing/shared_memory.py
+++ b/Lib/multiprocessing/shared_memory.py
@@ -433,9 +433,12 @@ def __setitem__(self, position, value):
 
         if not isinstance(value, (str, bytes)):
             new_format = self._types_mapping[type(value)]
+            encoded_value = value
         else:
-            if len(value) > self._allocated_bytes[position]:
-                raise ValueError("exceeds available storage for existing str")
+            encoded_value = (value.encode(_encoding)
+                             if isinstance(value, str) else value)
+            if len(encoded_value) > self._allocated_bytes[position]:
+                raise ValueError("bytes/str item exceeds available storage")
             if current_format[-1] == "s":
                 new_format = current_format
             else:
@@ -448,8 +451,7 @@ def __setitem__(self, position, value):
             new_format,
             value
         )
-        value = value.encode(_encoding) if isinstance(value, str) else value
-        struct.pack_into(new_format, self.shm.buf, offset, value)
+        struct.pack_into(new_format, self.shm.buf, offset, encoded_value)
 
     def __reduce__(self):
         return partial(self.__class__, name=self.shm.name), ()
diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index e64a8e9b3b8793..d5336e4d7be301 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -3964,9 +3964,21 @@ def test_shared_memory_ShareableList_basics(self):
         sl[4] = 'some'  # Change type at a given position.
         self.assertEqual(sl[4], 'some')
         self.assertEqual(sl.format, '8s8sdq8sxxxxxxx?q')
-        with self.assertRaises(ValueError):
-            sl[4] = 'far too many'  # Exceeds available storage.
+        with self.assertRaisesRegex(ValueError,
+                                    "exceeds available storage"):
+            sl[4] = 'far too many'
         self.assertEqual(sl[4], 'some')
+        sl[0] = 'encodés'  # Exactly 8 bytes of UTF-8 data
+        self.assertEqual(sl[0], 'encodés')
+        self.assertEqual(sl[1], b'HoWdY')  # no spillage
+        with self.assertRaisesRegex(ValueError,
+                                    "exceeds available storage"):
+            sl[0] = 'encodées'  # Exactly 9 bytes of UTF-8 data
+        self.assertEqual(sl[1], b'HoWdY')
+        with self.assertRaisesRegex(ValueError,
+                                    "exceeds available storage"):
+            sl[1] = b'123456789'
+        self.assertEqual(sl[1], b'HoWdY')
 
         # Exercise count().
         with warnings.catch_warnings():
diff --git a/Misc/NEWS.d/next/Library/2020-04-19-17-31-29.bpo-40330.DGjoIS.rst b/Misc/NEWS.d/next/Library/2020-04-19-17-31-29.bpo-40330.DGjoIS.rst
new file mode 100644
index 00000000000000..98cb62f1b115e3
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-04-19-17-31-29.bpo-40330.DGjoIS.rst
@@ -0,0 +1,2 @@
+In :meth:`ShareableList.__setitem__`, check the size of a new string item
+after encoding it to utf-8, not before.