The aim of this work is to present an enhanced kinematic plate model formulated according to the Mindlin-Reissner theory. The main function of the model is to simulate the behaviour of a plate structure up to failure taking into account energy dissipation in both membrane and flexural parts. First, the theoretical framework of the formulation is presented. Then, two kinematic enhancements are applied to the displacement and rotation fields by introducing two strong discontinuities fields. The first one is associated with the membrane displacement field and allows to describe the membrane failure, and the second one is introduced in the rotation field to describe the flexural failure. The embedded finite element method is used to incorporate the two kinematic discontinuities into a three-node plate finite element. The advantage of E-FEM lies in the possibility to statically condense these new variables at the local level an thus to preserve the architecture of the finite element code of interest. The kinematic and equilibrium operators associated with the enhancement variables are determined by satisfying specific conditions. The modelling of the failure process is carried out by means of traction-separation laws. The choice of this law has consequences on the response of the structure, therefore a sensitivity study with respect to the law is made. Elementary case studies are considered to assess the behaviour of the enhanced membrane component as well as the enhanced flexural component. The performance of the enhanced model is also illustrated through two structural casestudies: a single and a double notched concrete plates.