Organizations sometimes face critical situations or crises that can induce severe consequences or even disasters if wrong decisions are made. The bulk of crisis management research has relied heavily on case study methods yet often with rhetorical or even inconsistent suggestions. With an exclusive focus on crisis prevention, the issue of how organizations can maintain good performance when faced with critical situations has largely remained unexplored. There is also an apparent lack of consideration regarding how aspects of organizational design and task environment interact and affect organizational performance under critical situations. In this paper, we attempt to address this issue from an open system's perspective and integrate techniques of computational modeling with the analyses of two crisis cases, the Vincennes incident and the Hinsdale incident. The use of a computational model with strong organization theory foundation has provided a systematic mechanism for abstracting empirical information and generating theoretical results, thus complementing conventional case analyses, which thrive on in-depth information but are often limited by the lack of analytical ability to provide theoretical insight that goes beyond empirical descriptions. For the two crisis cases, the study shows, through detailed quantitative illustrations, that the computer model can be very effective in predicting organizational performance and suggesting designs that organizations can employ to mitigate the impact of crises. This study has demonstrated that our approach of computational case analysis can be very successful in providing systematic and explicit guidance for effective crisis mitigation both theoretically and empirically.