This article constructs a framework to help a decisionmaker allocate resources to increase his or her organization's resilience to a system disruption, where resilience is measured as a function of the average loss per unit time and the time needed to recover full functionality. Enhancing resilience prior to a disruption involves allocating resources from a fixed budget to reduce the value of one or both of these characteristics. We first look at characterizing the optimal resource allocations associated with several standard allocation functions. Because the resources are being allocated before the disruption, however, the initial loss and recovery time may not be known with certainty. We thus also apply the optimal resource allocation model for resilience to three models of uncertain disruptions: (1) independent probabilities, (2) dependent probabilities, and (3) unknown probabilities. The optimization model is applied to an example of increasing the resilience of an electric power network following Superstorm Sandy.