Compression loadings in thick composites can in some cases lead to three-dimensional states of stress with a compressive mean stress. A model is developed in the present work that attempts to incorporate this compressive mean stress into a prediction for compression strength of carbon/epoxy fiber composites. The model assumes that the fibers have an initial misalignment, and that composite failure occurs when the fiber-matrix bond strength is exceeded. Literature values for the effect of pressure on bond strength are included. Comparisons with experimental data support the predicted increase in compression strength with pressure.