Robots running on water have attracted the attention of researchers in the last decades as an alternative to conventional aquatic propulsion mechanisms. Up to now, a large scale robot capable of running on water has not been realized. Bouncing on water is a prerequisite for running on water. For this reason, the development of a water bouncing robot represents a necessary first step. The paper presents the model of a 2-degree-of-freedom water bouncing robot inspired by the pogo-stick, a device for jumping off the ground in a standing position. An analytical model of the impact force between “robot's foot” and water is provided for both water-entry and water-exit phases. Such a model has been integrated in a dynamic simulation of whole robot. The model represents a useful and general framework to gain an insight into the parameters that characterize the efficiency of robot.