In this paper, we propose a routing method for 2-layer ball grid array packages that generates a routing pattern satisfying a design rule. In our proposed method, the routing structure on each layer is restricted while keeping most of feasible patterns to efficiently obtain a feasible routing pattern. A routing pattern that satisfies the design rule is formulated as a mixed integer linear programming. In experiments with seven data, we obtain a routing pattern such that satisfies the design rule within a practical time by using a mixed integer linear programming solver.