Abstract: Based on the continuum damage mechanics, a 3D damage constitutive model which takes into account the nonlinear shear behavior of composites and material properties degradation due to damage development was proposed. The model differentiates between different failure modes, such as fiber failure mode, matrix failure mode and delamination. The damage variables corresponding to each failure mode were defined. The onsets of fiber damage, matrix damage and delamination of composite laminates were predicted using maximum stress failure criteria, Puck’s matrix failure criteria and Hou’s delamination criteria, respectively. In order to predict the angle of fracture surface in Puck’s matrix fracture failure theory, a selective parabola algorithm was proposed and coded using Matlab procedure. Compared with the Puck’s algorithm and the selective range golden section search algorithm, it shows that the selective parabola algorithm effectively reduces the number of calculations and improves the calculation efficiency and accuracy. A strain-driven explicit integration algorithm for the proposed material constitutive model was developed to update stresses and solution dependent state variables. The user-defined material subroutine VUMAT containing the numerical integration algorithm was coded and implemented in the finite element procedure Abaqus v6.14. The efficiency of the material constitutive model was demonstrated through progressive failure analyses of AS4 carbon fiber/3501-6 epoxy composite laminates, the mechanical behavior of which demonstrates significant nonlinear shear effects. The numerical results show that the proposed model is able to predict the mechanical behavior and failure strength of composites with sufficient accuracy. The proposed approach provides an efficient method for the design of composite components and structures.