static void Receive(object state)
{
    Socket socket = state as Socket;
    EndPoint otherEnd = new IPEndPoint(IPAddress.Any, 0);
    byte[] buffer = new byte[6400];
    try
    {
        socket.ReceiveFrom(buffer, ref otherEnd);
    }
    catch (SocketException se)
    {
        Console.WriteLine(se.Message);
    }
}
static void Main()
{
    Socket socket = new Socket(AddressFamily.InterNetwork, SocketType.Dgram, ProtocolType.Udp);
    socket.Bind(new IPEndPoint(IPAddress.Any, 12345));

    ThreadPool.QueueUserWorkItem(Receive, socket);
    Thread.Sleep(2 * 1000);

    socket.Shutdown(SocketShutdown.Both);
    socket.Close();                        //<---
    Console.WriteLine("socket closed");
    Console.ReadLine();
}

------解决方案--------------------

试试看异步吧

------解决方案--------------------

放个public static的变量，用于在下次receive前判断，
比如
while(true)
{
  if (var)
  {
   break;
  }

  receive...
}