High bandwidth and low latency switches are commercially available. Using these switches, it has become a popular and cost-effective way to interconnect workstations together as a parallel computing platform. The interconnection topology is usually irregular. On such systems, multicast is an important collective communication operation. In this paper, we study how to perform multicast on irregular switch-based networks assuming no special hardware support. Our proposed multicast algorithm is implemented completely at the software level by sending multiple unicast messages. We also prove that it is optimal in terms of the number of communication steps to accomplish the multicast without channel contention in each step. Performance of the proposed algorithm is evaluated by simulation.