In this work we illustrate how approximate dynamic programing can be utilized to address problems of stochastic reachability in infinite state and control spaces. In particular we focus on the reach-avoid problem and approximate the value function on a linear combination of radial basis functions. In this way we get significant computational advantages with which we obtain tractable solutions to problems that cannot be solved via generic space gridding due to the curse of dimensionality. Numerical simulations indicate that control policies coming as a result of approximating the value function of stochastic reachability problems achieve close to optimal performance. © 2013 EUCA.