In this paper we describe an algorithm for solving stochastic programs with simplerecourse, i.e.,generated by a linear programming problem with stochastic coefficients and a specific loss function (piecewise linear) associated with discrepancies observed between the output (Tx) and the resource vector. We show that this class of problems can actually be solved with about the same efficiency as solving linear programs of the same size. We first give a method for the discrete case and then indicate how recent approximation results can be used to obtain solutions whenthe random variables have a continuous distribution.