A distributed WWW caching system based on Internet Cache Protocol (ICP) is a system where a cache of a single proxy server is shared by others. When a proxy server receives an HTTP request for an object but it does not store the object locally in its cache, it sends queries to other proxies. However the system causes a problem that many ICP messages, i.e., IP packets, are exchanged between proxies. The increase of ICP packets puts high load on a router because it must look up its routing table to relay a packet. In this paper we focus on the number of packets on a distributed WWW caching system. We figure out the communication model of the system and influence of several parameters on the number of packets. Based on our model and the log data of an actual system, we reveal that ICP increases substantially the number of packets. Finally we conclude our argument with guidelines on organizing the distributed WWW caching system.