When structures undergo rotating motion, their modal characteristics often vary significantly. The variations of modal characteristics are determined from their geometric shapes and their rotating angular speed. Since the modal characteristics vary during the operation of the structures, they should be carefully scrutinized. In this paper, rotating cantilever beams are chosen as design targets which need to meet some specific design requirements. The thickness and the width of the rotating beams are assumed as multi-stage spline functions and the stage values for the thickness and the width are used as design variables for the optimization problems.