In this paper, we will present a study on a laminated composite material: Peek/APC2 with carbon fiber. We will treat the damage of this material in the framework of an elastoplastic model with isotropic and nonlinear kinematics hardening. The results of the simulations obtained using several approaches of this model (elasticity only, then coupled to plasticity with isotropic and nonlinear kinematics hardening) will be compared with the tests we made at the laboratory. The present model agrees qualitatively well with experiments for the nonlinear behavior as well as the presence of hysteresis loops in strain-stress diagrams. We also will stress that our numerical implementation highlights the significant influence of the fiber-matrix interface on the material damage modeling.