This study investigates the progressive failure analysis of composites by utilizing the Peridynamic Differential Operator (PDDO) for the solution of the equilibrium equations of Refined Zigzag Theory (RZT) without employing a stiffness degradation factor. In the derivation of equilibrium equations of RZT, the material property 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 first the verification of the solution method by comparison against an analytical solution and subsequently its demonstration by considering a symmetric cross-ply laminate with a through-the-thickness crack under tension.