Failure mode interactions when a laminated fiber reinforced composite is subjected to compression is studied here. Delamination, fiber kink-banding and their interaction are seen to dominate the failure response. An upscaled semi-homogenized laminate model is developed to predict the observed compression response of multi-directional laminates. A reduced 2-D formulation is presented first to determine the interfaces most susceptible to delamination. Subsequently, cohesive elements are added along these interfaces to introduce delamination capability in the model. Predictions of the model are compared against experimental data, and are found to be in agreement with respect to compressive strength and failure modes.