The hydraulic binary counter requires switching valves with a hysteretic response. In this paper an elastic snap through element is studied as means for that. The concept is based on a buckling beam which is elastically supported in axial direction in order to adjust its buckling properties with moderate manufacturing precision and to assure a well defined snap through behavior. The elastic support is provided by a cantilever beam. A rigorous optimization is performed heading for a most compact and fatigue durable design which exhibits the required lateral force displacement characteristics. A genetic algorithm is used to find the global design optimum. The stress/displacement properties of each design variant are computed by a compact model of the snap through system. It is derived by a Ritz method to obtain approximate solutions of the nonlinear buckling beam behavior. Its validity is checked by a Finite Element model. A compact design is possible if high strength spring steel is used for the elastic elements.