Abstract A finite element (FE) model, which includes in-ply and delamination damage effects, is developed for the progressive failure analysis of composite laminates. A combined elastoplastic damage model which accounts for both plasticity and damage effects is used to represent the mechanical response of composite layers and is implemented in the FE code Abaqus using user-defined material subroutine UMAT. A cohesive zone model based on cohesive elements available in Abaqus is employed to simulate delamination behaviour in the adhesive interfaces. Continuum shell elements and cohesive elements are stacked together to simulate composite and adhesive layers, respectively. The model is applied to the progressive failure analysis of AS4/PEEK composite laminates subjected to in-plane tensile and out-of-plane transverse low-velocity impact loadings. It is shown that the model can be successfully applied to the simulations of composite laminates susceptible to delamination failure.