This paper showcases the authors’ predictions for the 13 challenging test cases of the third World Wide Failure Exercise. The cases involve the prediction of lamina biaxial stress–strain curves, matrix cracking and delamination in various cross-ply and quasi-isotropic laminates under uniaxial loading, variation of thermal expansion coefficient of a laminate with matrix cracking, bending of a general laminate, loading-unloading behaviour and the strength of various thin and thick laminates containing an open hole. The laminates were made of various glass and carbon fibre/epoxy materials. The constitutive model is based on plasticity theory, includes hydrostatic pressure effects and accounts for multiaxial load combination effects. The failure criteria distinguish between matrix failure, fibre kinking and fibre tensile failure. In-situ strengths are used for matrix failure. Propagation of failure takes into consideration the fracture energy associated with each failure mode and, for matrix failure, the accumulation of cracks in the plies. The model is used to make blind predictions of all test cases from the third World-Wide Failure Exercise.