This paper examines the application of a cohesive zone model to predict the open hole compressive strength of an IM7/8552 carbon fibre/epoxy quasi-isotropic multidirectional laminate and investigates the level-ply scaling or ply blocking effect on notch sensitivity. Cohesive zone models have been successfully applied to predict the damage from notches in engineering materials loaded in tension. They have also been used to determine the growth of fibre microbuckling from a hole in composite laminates under compression. The usual strategy is to replace the inelastic deformation associated with plasticity or microbuckling with a line-crack and to assume some form of stress-displacement ( - ) bridging law across the crack faces. Here a plastic fibre kinking analysis and a linear reduced (softening) - relationship are used for the prediction of the unnotched and open hole compressive strength; the theoretical results will be compared with experimental data in Part B of the 3rd World-Wide Failure Exercise.