We propose a computational approach to approximate the value function and control poli- cies for a finite horizon stochastic reach-avoid problem as follows. First, we formulate an infinite dimensional linear program whose solution characterizes the optimal value function of the stochastic reach-avoid. Next, we introduce sum-of-squares polynomials to approxi- mate the solution of this linear program through a semidefinite program. We compare our proposed tool to alternative numerical approaches via several case studie.