Effect of fibers alignment on the failure of composites in compression in the fiber direction. This work deals with the measurement and modeling of compressive strength in the fiber direction for unidirectional carbon/epoxy composite, and focuses on the influence of the global misalignment angle of the fibers. At first, from previous experimental results, it is shown that the presence of diffuse damage in the matrix significantly modify the compressive strength. A mesoscale model based on matrix damage variable is given to account for the phenomenon. Secondly, these results are applied to the case of specimens with global misalignment angle. It will be shown that in this case, the problem becomes complex since misalignment of the fibers and matrix damage are coupled. Finally, from an original compression test specimens with stress concentration, we show the interest to take into account the matrix damage state for predicting the failure.