The tremendous growth of the Internet coupled with newly emerging applications has created a vital need for multicast traffic support by backbone routers and ATM switches. Considerable research work has been done on Input Queued (IQ) switches to handle multicast traffic flows. Unfortunately, all previously proposed solutions were of no practical value because they either lack performance or were simply too complex to implement. Internally Buffered Crossbar (IBC) switches, where a limited small amount of memory is added in each crosspoint of the crossbar fabric, on the other hand, have been considered as a robust alternative to buffer-less crossbar switches to improve the switching performance. However, very little has been done on multicasting in IBC switches. In this paper, we fill this gap and study the multicasting problem in IBC switches. In particular, we propose a novel IBC based multicast architecture along with a simple scheduling scheme named Multicast cross-point Round Robin (MXRR). Our scheme was shown to handle multicast traffic more efficiently and far better than all previous schemes for both the multicast FIFO architecture as well as the multicast k FIFO queues architecture. Yet, MXRR is both practical and achieves high performance.