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This article presents a reliability-based evacuation route planning model that seeks to find the relationship between the clearance time, number of evacuation paths, and congestion probability during an evacuation. Most of the existing models for network evacuation assume deterministic capacity estimates for road links without taking into account the uncertainty in capacities induced by myriad external conditions. Only a handful of models exist in the literature that account for capacity uncertainty of road links. A dynamic network–based evacuation model is extended by incorporating probabilistic arc capacity constraints and a minimum-cost network flow problem is formulated that finds a lower bound on the clearance time within the framework of a chance-constrained programming technique. Network breakdown minimization principles for traffic flow in evacuation planning problem are applied and a path-based evacuation routing and scheduling model is formulated. Given the horizon time for evacuation, the model selects the evacuation paths and finds flows on the selected paths that result in the minimum congestion in the network along with the reliability of the evacuation plan. Numerical examples are presented and the effectiveness of the stochastic models in evacuation planning is discussed. It is shown that the reliability-based evacuation plan is conservative compared with plans made using a deterministic model. Stochastic models guarantee that congestion can be avoided with a higher confidence level at the cost of an increased clearance time.