Abstract: Failure evolution in composite structures under compression is a fundamental topic and plays a key role in the strength prediction of composites. Herein, a progressive damage analysis (PDA) model based on continuum damage mechanics (CDM) was proposed to analyze the compression failure of unidirectional fiber reinforced polymer composites. Some essential issues such as the nonlinear behavior of composites, failure judgement, and the degradation of material properties during damage evolution were considered, corresponding respectively to the tension-compression asymmetric elasto-plastic constitutive model, Puck criteria, LaRC05 criteria and a stiffness degradation model considering the direction of fracture plane. The proposed PDA model was implemented in finite element analysis (FEA) by using the interface of user defined materials subroutine (VUMAT) provided by ABAQUS. The result of FEA is in good agreement with the experiment data reported by literatures in the cases of longitudinal, transverse and off-axis compression, which proves the reasonability and effectiveness of this PDA model. This work is of great reference value for compression failure analysis of multidirectional laminates.