This paper presents a new modeling approach based on peridynamic (PD) theory for progressive failure analysis of composites. It is not limited to specific fiber orientation and material properties. It also enables the evaluation of stress and strain fields in each ply of the laminate. Therefore, it permits the use of existing stress-or strain-based failure criteria for damage prediction. The force density vectors in the PD equation of motion are derived explicitly for in-plane, transverse normal and transverse shear deformations in terms of the engineering material constants. The PD bonds enable the interaction of material points within each ply as well as their interaction with other material points in the adjacent plies. The PD equilibrium equation is solved by employing implicit techniques in an iterative form to account for damage progression based on the Hashin failure criteria. The capability of this approach is verified by comparing the deformation field of a lamina and a unidirectional laminate for varying fiber orientations, and nonsymmetric laminates against the finite element results in the absence of failure. Also, the PD predictions for progressive failure in a lamina with a pre-existing crack capture the experimental observations.