To overcome the inaccurate estimations of local response near free-edges of equivalent single-layer the-ories, a collection of layerwise models have been developed by the Navier laboratory in which the in-terlaminar shear stress is one of the generalized forces [1, 2]. The latest one (SCLS1) with first-ordermembrane stresses is considered in this work. The laminated plate is considered as a superposition ofReissner-Mindlin plates coupled by shear and normal interface stresses. The model ensures an accurateestimation of the shear stress and respect the free edge boundary conditions.First the equations of the SCLS1 model are derived from the 3D Cauchy model under the assumption ofpiecewise linear membrane stress. The model is then built by satisfying the 3D equilibrium equations.The problem is numericaly solved by a standard displacement finite element methods. The generalizeddisplacements are the Lagrange multipliers of each equilibrium equations. A variational damage for-mulation is then used to predict the initialization and the propagation of the delamination between tworelated plies. The delamination is driven by 2nscalar variables which lower the interfacial stress to zero.In order to manage the evolution of these scalar variables, we postulate that the potential energy is dividedbetween the strain energy and an interfacial fracture energyEpot(u,d) =EΩel(u)+EΓF(d)−Wext. The pairdisplacement-damage(u,d)is found using an incremental strategy⇒stationarity of the potential energyunder the constraint of strict growth of the damage variables: (u,d) =arg mind;d≥dnEpot(u,d)A double cantilever beam problem is considered to evaluate the accuracy of such models. An analyticalsolution given by linear fracture mechanics is used to validate our approach. All the simulations havebeen implemented using the open source FEniCS platform for solving partial differential equations.