Abstract: We study a multistage ATM switch in which shared-memory switching elements are arranged in a banyan topology. By "shared memory", we mean that each switching element uses output queueing and shares its local cell buffer memory among all its output ports. We apply a buffer management technique called delayed pushout that was originally designed for multistage ATM switches with hierarchical topologies. Delayed pushout combines a pushout mechanism, for sharing memory efficiently among queues within the same switching element, and a backpressure mechanism, for sharing memory across switch stages. The backpressure component has a threshold to restrict the amount of sharing between stages. A synergy emerges when pushout, backpressure, and this threshold are all employed together. Using a computer simulation of the switch under bursty traffic, we study delayed pushout as well as several simpler pushout and backpressure schemes under a variety of traffic conditions. Of the five schemes we simulate, delayed pushout is the only one that performs well under all load conditions.