This study addressed the stochastic physical distribution network design problem, considering demand randomness, economies of scale in transportation costs, and supply shortage/surplus at facilities in order to reflect the practical operations. The problem is formulated as a two-stage stochastic program. The objective function is to minimize the total cost and the decisions are to determine the optimal facility location, distribution network, flow allocation, and supply shortage/surplus at facilities. In order to enable the application in the real-size large-scale problem, a solution algorithm based on the Sample Average Approximation technique was developed to solve the proposed model. An illustrative example was created to test the proposed model and solution algorithm. The results show that the model is practically implementable and the algorithm is efficient while ensuring the quality of solution.