This study applies the Peridynamic Differential Operator (PDDO) to solve for the equilibrium equations of Classical Laminate Theory (CLT) for progressive failure analysis of composites without employing a stiffness degradation factor. The PD representation of the displacement derivatives and the transformed reduced stiffness matrix permits the evolution of fiber and matrix cracking during deformation, and enables the modeling of progressive failure. In the derivation of equilibrium equations of CLT, the transformed reduced stiffness matrix is considered as spatially varying unlike the common assumption of its uniform variation. The PD representation of these equations enables the modeling of progressive failure during the deformation through the removal of PD interactions (bonds). The stiffness degradation is natural, and it is achieved by removing the PD bonds. The numerical results concern unidirectional laminates and a symmetric cross-ply laminate with a through-the-thickness crack under tension, and a non-symmetric cross-ply laminate with a crack only in the bottom ply subjected to a uniform distributed load.