This research focuses on studying the effect of the constitutive law adopted for a matrix material on the compressive response of a unidirectional fiber reinforced polymer matrix composite. To investigate this effect, a periodic unit cell model of a unidirectional composite with an initial fiber waviness and inelastic behavior of the matrix was used. The sensitivity of the compressive strength to the hydrostatic pressure, the flow rule and the fiber misalignment angle were presented. The model was verified against an analytical solution and experimental data. Results of this study indicate that a micromechanical model with correctly identified material parameters provides a useful alternative to theoretical models and experimentation.