In this paper, we propose the input-buffered replicated self-routing switch model with multiple priority classes in order to satisfy different demands of several traffic cell classes. The priority path setup discipline at each switching element is proposed in order to perform priority path setup when two cells of higher-and lower-priority classes arrive at the switching element. The nonpreemptive priority discipline at the external input buffers outside the switch for each class of cells is employed so that a higherpriority cell is served first at the head of the line (HOL), whereas it has to wait in the buffer until the completion of the low-priority cell in service. We analyze the system delay of every priority class cell for the random sharing model which distributes the cells randomly on the R planes, as well as the alternate sharing model which avoids contentions in the first log 2 R stages of each plane which serves Bernoulli arrival cells. Furthermore, when the buffer size for high-priority cells is limited, we consider the relation between the cell loss probability and input buffer sizes for two classes, and obtain the proper buffer size for the high-priority cells by computer simulation. It is seen that the proposed model is effective in showing the priority for different class cells.