Contingency firelines can be used to back up primary lines to increase probability of fire containment, decrease fire losses, and improve firefighter safety. In this study, we classify firelines into primary, contingency, and response lines. We design a modeling process to iteratively implement a mixed integer programming model to evaluate contingency strategies under randomly generated fireline breaching scenarios. Our objectives include: (1) gaining conceptual understanding of the effectiveness of using contingency containers in a fireline network, and (2) suggesting future data collection and model improvement directions to support contingency strategy planning. We evaluate the effectiveness of several model generated containment strategies: only responding to observed primary line breaches, being proactive by implementing a system‐level contingency plan, or constructing contingency lines to back up a proportion of a primary container. Data from the Ferguson Fire in California are used to derive a set of hypothetical test cases with different fireline breaching risks to support sensitivity analysis. For comparison, we also test a contingency plan inspired by the Ferguson Fire operation. Analyses suggest that a contingency plan will provide the greatest benefit when fireline breaching risk is high. This study also suggests there are significant data and knowledge gaps that must be addressed to make the model suitable for operational use.