A cost minimization model for designing AS/RS (Automated Storage/Retrieval Systems) has been developed, whose objective function includes penalty cost caused by the incapability of meeting throughput rate requirements as well as S/R machine cost, storage rack cost, and interface conveyor cost. Since the model is a nonlinear integer programming problem which is very hard to solve with large problem size the problem is divided into four cases according to the ratio of horizontal S/R machine speed to its vertical speed and the existence of the penalty cost. A solution procedure is developed which solves each problem exactly under the different number of S/R machines.