On modelling the residual strength of impact damaged, compression loaded laminatesA methodology is presented to predict the residual compression strength of impact damaged composite laminates by considering the competing failure modes of local delamination buckling and compression failure. The minimum delamination buckling load and the location of the first local region to buckle are determined by a Rayleigh-Ritz analysis. The Rayleigh-Ritz analysis is formulated to account for the multiple delamination locations, Poisson's ratio mismatch between sublaminates and possible bending-stretching coupling behavior of the delaminated regions. The compression failure load is determined by a modified maximum strain criterion applied in the delaminated region. The minimum delamination buckling and compression failure loads may be compared to the global buckling load to predict initial failure. For non-catastrophic failures, failure sequences are predicted in an iterative manner. Analytical predictions for sequential failure modes and loads are shown to correlate well with experimental results. A comparative evaluation of various delamination buckling models and their accuracy in predicting experimental results is also presented.