A quasi-brittle damage model for composite material is presented to analyze progressive failure in composite structures. A rate independent constitutive law is expressed in terms of three damage parameters by using several polynomial failure criteria and a suitable micromechanical model. In order to follow the damage evolution of laminated composite plates subject to monotonic loads, a numerical procedure, based on a finite element approximation, is developed. In particular, the material stiffness reduction is computed by the proposed damage model and the number of global degrees of freedom is reduced by using `clusters of laminae'. Finally, both numerical and experimental data available in literature are compared with the results obtained by the proposed numerical procedure.