Modern society is critically dependent on the services provided by engineered infrastructure networks. When natural disasters (e.g. Hurricane Sandy) occur, the abil-ity of these networks to provide service is often de-graded because of physical damage to network com-ponents. One of the most critical of these networks is the electrical distribution grid, with medium voltage circuits often suffering the most severe damage. How-ever, well-placed upgrades to these distribution grids can greatly improve post-event network performance. We formulate an optimal electrical distribution grid de-sign problem as a two-stage, stochastic mixed-integer program with damage scenarios from natural disas-ters modeled as a set of stochastic events. We develop and investigate the tractability of an exact and several heuristic algorithms based on decompositions that are hybrids of techniques developed by the AI and opera-tions research communities. We provide computational evidence that these algorithms have significant benefits when compared with commercial, mixed-integer pro-gramming software.