The response of polymer matrix composites under combined proportional axial and torsional loading has been studied. Experiments were performed on solid cylindrical specimens of glass/vinylester and carbon/vinylester composites at a fiber volume fraction, Vf equal to 50%. The specimens were loaded under displacement and rotation control in a proportional manner. The Budiansky-Fleck kinking model was specialized to the case of a solid cylindrical specimen and the predictions were compared to the experimental results. It was found that the compression strength of carbon composites is approximately a linear function of the applied rotation but in the case of glass composites the compression strength is initially unaffected due to shear. At a critical value of shear, the compression strength is seen to diminish rapidly. This suggests that the Budiansky-Fleck model might not be suitable for predicting the effect of shear on compression strength of glass fiber composites.