The present work proposes a model to predict the compression strength of CFRP as a function of various material characteristics: fiber properties and volume content, non-linear matrix properties, interface properties, residual strains, fiber misalignment, ply waviness, and interlaminar properties. For this, a three-step FE-based approach is developed considering (i) fiber microbuckling, (ii) wavy ply mesobuckling, and (iii) the mutual influence of these two. This approach is then applied to investigate the relative contribution of the mentioned material characteristics on compression strength deficits of NCF (Non-crimp Fabric) CFRP with respect to prepreg, in order to identify ways to improve NCF performance.