In this paper, we present a new design to support multicasting in an ATM switches, called the Singlecast Stuffed Multicast Advanced Processing (SSMAP) ATM switch, which can transmit multicast traffic effectively. The SSMAP ATM switch consists of two cell operation parts, a multicast operation part and a singlecast operation part. This structure is designed so as to increase the efficiency of packet forwarding by allowing singlecast cells to use the resources that remain unused during multicast traffic handling. Furthermore, we propose new multicast scheduling methods using the SSMAP ATM switch. We evaluate the characteristics of the SSMAP ATM switch and multicast scheduling methods by computer simulations, and demonstrate their validity.