1There are two design challenges of the flow path switching valve in a three-stage variable discharge oil pump. The first is to obtain the required discharge pressure characteristics and the other is to prevent hydraulic vibration. Therefore, we established technologies to determine the shape of the valve and the valve housing that resolve these two challenges.The technology to obtain the required discharge pressure characteristics solves equations that are statically true, such as the equations for the equilibrium of forces and hydraulic orifice. The hydraulic vibration control technology derives a differential equation that takes transient behavior, including oil elasticity and inertia, into account first. Then, the derived equations are converted to a transfer function that indicates the valve behavior according to the input of oil pressure changes. And then the stability criterion is applied to judge whether hydraulic vibration occurs or not.By combining these technologies and an optimization technology, the shape of the valve and the valve housing that realizes the downsizing idea was determined.