A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave as elastic-plastic and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter. The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina, the fiber and inplane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed constitutive model is tested against experimental data and good agreement is obtained. Then, numerical analyses are performed to study the failure behavior of symmetric angle-ply composite laminates and symmetric cross-ply composite laminates subjected to biaxial loads. Finally, the conclusions obtained from the numerical analysis are given.