A new multicasting mechanism for RAM-based shared-buffer ATM switches is introduced. Multiple logical output queues, including a new queue for multicast and broadcast cells, are all interleaved into a single physical buffer as in the single-queue switch architecture. Queues are hardware-independent and full buffer-sharing is achieved. Cells are scheduled in the multicast queue based on their priority level and service type as in the unicast queues. A single copy of a multicast cell is kept in the queue. The cell is sent to all of its destinations upon its service time. A unicast cell in a given output queue can still be sent if it has higher priority than a multicast cell. In this case a unicast copy of the multicast cell for that output port is placed in the output queue. This copying scheme requires neither extra hardware nor extra memory space for duplicated cells. A new grouping algorithm is presented which supports the incorporation of the multicast queue and the unicast queues into a single overall queue.