We investigate a dynamic packet routing approach to ATM switch design using a hypercube. An (n+1)-dimensional hypercube is used to implement an N/spl times/N switch, where N=2/sup n/. Cells arriving at input ports are routed towards their destinations in store-and-forward (SAF) manner. In addition to the SAF buffer, each input/output port has a dedicated buffer. A distributed deflection routing algorithm where the routing priority is based on the age of the cells is developed. An interesting feature of the routing algorithm is that the store-and-forward buffers and the input buffers behave as distributed shared-buffer which effectively smooth out uneven traffic. In addition, our routing algorithm does not suffer from the HOL blocking problem as in the conventional input-output buffered switch architecture. The processing power of each node in the hypercube scales up by a factor of Q(log N) as the network size N is increased. Hence, our approach is suitable for implementing large scale ATM switches. Performance of our design is studied via simulation and found to be better than the conventional input-output buffered nonblocking switch architecture.