Polymer matrix composites (PMCs) are widely used in various industries, including aerospace, vehicles, sports utilities, and civil infrastructures. Understanding the failure process and mechanisms of PMCs subjected to external loads is crucial for their reliability. This study aims to develop a semi-analytic stress-function variational method for accurate prediction of interfacial stresses and progressive cracking in PMC laminates. The method uses a three-layered cross-ply laminate model with periodic transverse ply cracks, introducing two unknown interfacial shear and normal stress functions at each laminate interface. The stress field is expressed in terms of these stress functions, using Euler-Bernoulli beam theory and elasticity. The method also considers transverse deflections of the plies, resulting in accurate predictions of interface stresses. The method can be used for scaling analysis of interfacial stresses and progressive cracking in PMC laminates as validated by finite element analysis (FEA).