In this paper, a model of laminated plates called M4-5N and validated in a previous paper is modified in order to take into account interlaminar plasticity by means of displacement discontinuities at the interfaces. These discontinuities are calculated by adapting a 3D plasticity model. In order to compute the model, a Newton–Raphson-like method is employed. In this method, two sub-problems are considered: one is linear and the other is non-linear. In the linear problem the non-linear equations of the model are linearized and the calculations are performed by making use of a finite element software. By iterating the resolution of each sub-problem, one obtains after convergence the solution of the global problem. The model is then applied to the problem of a double lap, adhesively bonded joint subjected to a tensile load. The adhesive layer is modeled by an elastic–plastic interface. The results of the M4-5N model are compared with those of a commercial finite element software. A good agreement between the two computation techniques is obtained and validates the non-linear calculations proposed in this paper. Finally, the numerical tool and a delamination criterion are applied to predict delamination onset in composite laminates.