The frame structure of a motor cycle is required to be as rigid and as light as possible. In this paper, the minimum compliance design of the frame structure of a motor cycle is treated numerically. Torsional rigidity between the head pipe and swing arm pivots, which is very important for the driving stability of a motor cycle, is maximized under constraints of the total volume. Two typical cases of design are implemented. In the first case, cross-sectional areas of the frame members are taken as design variables. Shape optimization of the frame structure subjected to geometrical constraints, which are caused by keeping the driving function and the space of some parts, is carried out in the second case. In the latter case, positions and cross-sectional areas of frame members are varied simultaneously. Rigid and simple frame structures of the motor cycle are obtained for each design problem.