We consider the optimization of multi-period linear planning models with stochastic parameters (e.g., costs, demands, and supplies). The stochastic parameters are characterized by discrete probability distributions defined over a finite probability space. We formulate the mathematical problem as a multistage stochastic programming problem with recourse. This problem is known to exhibit exponential growth in size and thus is considered intractable for all but small cases. In this paper we address the two-stage problem. A successive repartitioning algorithm is developed and solution results are compared with the alternative solution methods, variants of Benders decomposition schemes tailored to the dynamic staircase LP structure. The partitioning algorithm is guaranteed to converge to the exact solution in a finite number of iterations, and has a highly parallel decomposition and computer implementation. Example problems are presented to demonstrate the solution technique and to provide a comparison with the Benders-based methods.