Summary: An important task in structural analysis is the identification of critical structure collapse mechanisms, that is, given a structural design and loading configuration, determine which failure mechanisms will occur first. In this work, we extend traditional deterministic optimization models for failure mode identification to stochastic forms by considering external loads and structural member plastic moment capacities as correlated random variables. A hybrid model is first developed that contains both chance constrained programming and stochastic linear programming features. A purely chance constrained model is then described. Both models represented nonconvex programming problems. Computational experience with the models is described through an application to the analysis of a portal frame.