The provision of structural integrity to avoid major failure and progressive collapse of buildings under abnormal loading is a major concern for design engineers. Current codes and standards that deal with this issue often propose only qualitative criteria. As well, there is generally no consensus among researchers and engineers concerning performance-based requirements for design against progressive collapse. One of the major reasons seems to be the difficulty and complexity of the collapse analysis of buildings. This paper proposes some simplified methods for the analysis of building structures subjected to abnormal loads that result in structural collapse. The computational techniques can be used to track possible failure mechanisms and give useful information to the designer about the integrity of the structure. The proposed methods are based on simple linear analysis and can easily be implemented in conventional commercially-available engineering analysis and design software for building structural systems. The results of the simplified methods are verified through comparison with those found using rigorous nonlinear failure analysis.