Nanocomposites with platelet reinforcements are emergent materials whose deformation mechanisms still need to be carefully investigated. In this study, we first present the studied class of nanocomposites (Polypropylene reinforced by Montmorillonite clay nanoplatelets). From uniaxial tensile tests, it is shown that some mechanical characteristics of the nanocomposite (Young's modulus, yield stress) significantly increase compared to the matrix even for very low volume fraction of reinforcements (maximum of 7% mass fraction for our tested specimen). The Ponte Castañeda and Willis [6] bound is adopted to account for the evolution of the elastic behavior of the material [7]. Adapting the Hill-type incremental method [13] allows the simulation of the non linear behaviour of the material. However, it is shown that this scheme requires careful choice of the aspect ratio, in the plastic domain, to provide good predictions of plasticity.