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Currently, many bandwidth-intensive applications require multicast services for efficiency purposes. In particular, as wavelength division multiplexing (WDM) technique emerges as a promising solution to meet the rapidly growing demands on bandwidth in present communication networks, supporting multicast at the WDM layer becomes an important yet challenging issue. In this paper, we present a new analytical model to compute blocking probabilities for multicast connections in WDM switching networks. Due to the non-uniform nature of multicast traffic, calculating blocking probability in a WDM multicast switching network becomes much more challenging than that under unicast traffic. Based on the link independence and wavelength independence assumptions, our model can calculate the blocking probability of any multicast connection from a single source to multiple destinations in WDM switching networks with various types of wavelength conversion capabilities, ranging from no wavelength conversion, to limited wavelength conversion, to full wavelength conversion. Our analytical results indicate that similar to unicast traffic, a significant improvement in the blocking performance of the network under multicast traffic can be achieved by limited wavelength conversion. We view that utilizing limited wavelength conversion with relatively small conversion degrees in WDM multicast switching networks is a more cost-effective choice. We also validate the analytical model through extensive simulations.