In this paper, we develop a design model for a system of an automated warehouse with aisles, between which there is a stacker crane running through both vertically and horizontally at one command. The problem is formulated as a nonlinear mixed integer programme in which the cost of the system is minimized with required functions of the automated warehouse. A method of solution is given on the basis of non-linear programming techniques. We also make a trade-off analysis between cost and functions. By doing this, automated warehouses can be designed more flexibly and more efficiently. Some experiments prove the efficiency of the method.