Multicast network traffic is information with one source node, but many destination nodes. Rather than setting up individual connections between the source node and each destination node, or broadcasting the information to the entire network, multicasting efficiently exploits link capacity by allowing the source node to transmit a small number of copies of the information to mutually-exclusive groups of destination nodes. Multicasting is an important topic in the fields of networking (video and audio conferencing, video on demand, local-area network interconnection) and computer architecture (cache coherency, multiprocessor message passing). In this paper, we derive approximate expressions for the minimum cost (in terms of link utilization) of shortest-path multicast traffic in arbitrary tree networks. Our results provide a theoretical best-case scenario for link utilization of multicast distribution in tree topologies overlaid onto arbitrary graphs. In real networks such as the Internet MBONE, multicast distribution paths are often tree-like, but contain some cycles for purposes of fault tolerance. We find that even for richly-connected graphs such as the shufflenet and the hypercube, our expression provides a good prediction of the cost (in terms of link utilization) of multicast communication. Thus, this theoretical result has two applications: (1) a lower bound on the link capacity required for multicasting in random tree topologies, and (2) an approximation of the cost of multicasting in regular LAN and MAN topologies.