diff --git a/Lib/test/support/__init__.py b/Lib/test/support/__init__.py
index 1c6ee03..1ab2136 100644
--- a/Lib/test/support/__init__.py
+++ b/Lib/test/support/__init__.py
@@ -601,8 +601,14 @@
 # Windows limit seems to be around 512 B, and many Unix kernels have a
 # 64 KiB pipe buffer size or 16 * PAGE_SIZE: take a few megs to be sure.
 # (see issue #17835 for a discussion of this number).
-PIPE_MAX_SIZE = 4 *1024 * 1024 + 1
+PIPE_MAX_SIZE = 4 * 1024 * 1024 + 1
 
+# A constant likely larger than the underlying OS socket buffer size, to make
+# writes blocking.
+# The socket buffer sizes can usually be tuned system-wide (e.g. through sysctl
+# on Linux), or on a per-socket basis (SO_SNDBUF/SO_RCVBUF). See issue #18643
+# for a discussion of this number).
+SOCK_MAX_SIZE = 16 * 1024 * 1024 + 1
 
 # decorator for skipping tests on non-IEEE 754 platforms
 requires_IEEE_754 = unittest.skipUnless(
diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 9567090..b95e1ab 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -1210,11 +1210,12 @@
                 c.settimeout(1.5)
             with self.assertRaises(ZeroDivisionError):
                 signal.alarm(1)
-                c.sendall(b"x" * (1024**2))
+                c.sendall(b"x" * support.SOCK_MAX_SIZE)
             if with_timeout:
                 signal.signal(signal.SIGALRM, ok_handler)
                 signal.alarm(1)
-                self.assertRaises(socket.timeout, c.sendall, b"x" * (1024**2))
+                self.assertRaises(socket.timeout, c.sendall,
+                                  b"x" * support.SOCK_MAX_SIZE)
         finally:
             signal.alarm(0)
             signal.signal(signal.SIGALRM, old_alarm)
@@ -4047,7 +4048,7 @@
         self.serv_skipped = None
         self.serv_conn.setblocking(False)
         # Try to saturate the socket buffer pipe with repeated large writes.
-        BIG = b"x" * (1024 ** 2)
+        BIG = b"x" * support.SOCK_MAX_SIZE
         LIMIT = 10
         # The first write() succeeds since a chunk of data can be buffered
         n = self.write_file.write(BIG)