The design of resilient supply chains under the risk of disruptions at candidate locations for distribution centers (DCs) is formulated as a two-stage stochastic program. The problem involves selecting DC locations, determining storage capacities for multiple commodities, and establishing the distribution strategy in scenarios that describe disruptions at potential DCs. The objective is to minimize the sum of investment cost and expected distribution cost during a finite time horizon. The rapid growth in the number of scenarios requires the development of an effective method to solve large-scale problems. The method includes a strengthened multicut Benders decomposition algorithm and the derivation of deterministic bounds based on the optimal solution over reduced sets of scenarios. Resilient designs for a large-scale example and an industrial supply chain are found with the proposed method. The results demonstrate the importance of including DC capacity in the design problem and anticipating the distribution strategy in adverse scenarios.