Many uncertain factors have an influence on a supply chain network design problem, including market demands, product prices, and costs. Many conventional approaches assume that market demands are known and deterministic. Furthermore, the objective functions of supply chain network design problems are mainly to minimize total costs or to maximize total profit. Uncertainty and induced risk of profit variations are often disregarded. In this study, we apply the robust optimization technique to explore a multiple-product supply chain network design problem with stochastic customer demands. The optimal locations of factories, locations of distribution centers, and production volume of each commodity of each factory are simultaneously determined in the proposed model. In order to assure the robustness of the supply chain network, the objective is to minimize a weighted sum of total expected costs, variability of total expected costs, and infeasibility penalties of system constraints. Herein, total expected cost is the sum of total production costs, total transportation costs, total operation costs of distribution centers, and total inventory costs of distribution centers. A sampling-based algorithm, sampling average approximation method, is adopted to find the heuristic solution of the proposed model. Finally, numerical examples are elaborated and sensitivity analyses are utilized for demonstrating the rationality and practicality of the proposed model.