Based on the continuum damage mechanics theory and Gibbs free energy principle, a two dimensional progressive damage model is built to describe the damage and failure process of composite laminates under the plane stress state. This damage mode is combined with the Hashin damage criterion and coded by the ABAQUS user subroutine as a new damage constitutive model for composite laminates. To verify its capacity, a FE model with above damage constitutive is applied to analyze the damage onset and propagation of the composite laminates with centric cutout and compared with the experimental, and the comparable results shows the above damage constitutive has relative high capability in describing the laminates structural damage propagation processes. This material model is further used to study damage evolution in different layers for laminates with three different cutout-shapes under the shear load, and the results shows the cutout-shape has very sensitive influence in damage and failure processes of composite laminates.