|Critical infrastructure systems provide essential services that support modern society. However, these systems are deteriorating and becoming more vulnerable to multiple hazards. In order to improve their resilience (i.e., ability of a system to respond to and recovery from disasters), there is a critical need to assess infrastructure performance during disruptions. Assessing the resilience of infrastructure systems is subject to multiple sources of uncertainty, such as the hazard type, component vulnerability, recovery behavior, and the interdependency across infrastructure systems. Improper characterization of multiple sources of uncertainty in resilience modeling of infrastructure systems results in under- or over-estimation of system performance and a suboptimal allocation of resources in preparedness and restoration strategies. This dissertation applies and develops Bayesian and stochastic network methods to model interdependencies, evaluate system serviceability, predict resilience metrics, and optimize system resilience of critical infrastructure under uncertainty. The proposed approaches are illustrated with case studies of real and simulated interdependent water, power, and gas networks. The developed methods and analyses can be used to guide infrastructure operators and decision-makers in the allocation of resources before, during, and after a disaster.