Packet-switched unidirectional and bidirectional ring wavelength division multiplexing (WDM) networks with destination stripping provide an increased capacity due to spatial wavelength reuse. Besides unicast traffic, future destination stripping ring WDM networks also need to support multicast traffic efficiently. In this paper, we provide a probabilistic analysis of the mean hop distances travelled by multicast packet copies on the wavelength channels, and based on the mean hop distances analyze the nominal transmission capacity, reception capacity, and multicast capacity of both unidirectional and bidirectional ring WDM networks with destination stripping. The developed analytical methodology accommodates not only multicast traffic with arbitrary multicast fanout but also unicast and broadcast traffic. In our numerical investigations we examine the impact of number of ring nodes and multicast fanout on the transmission, reception, and multicast capacity of both types of ring networks for different unicast, multicast, and broadcast traffic scenarios and different mixes of unicast and multicast traffic. Our analytical methodology provides a foundation for extended analyses of the multicast capacity of WDM ring networks and enables the evaluation and comparison of future multicast-capable medium access control (MAC) protocols for unidirectional and bidirectional ring WDM networks in terms of transmitter, receiver, and multicast throughput efficiency.