The Random Waypoint model is a commonly used mobility model in the field of ad hoc network. The spatial probabilistic distribution of this mobility model is deeply studied, and the exact spatial distribution function of the generalized model with pause time and velocity randomly chosen has been obtained both in 1D and 2D region. Simulation results have also validated the distribution functions. Through the exact function it could be seen how pause time and velocity affect the node spatial distribution. The research results provide theoretical foundations for derivations and proofs of ad hoc theories based on the Random Waypoint mobility model. Also the exact distribution is of practical significance in conducting the simulations of performance evaluation based on the Random Waypoint model.