||This paper is concerned with the asymptotic analysis of plates with periodically radidly varying heterogeneities. The asymptotic analysis is performed when both the material properties and the thickness of the plate are of the same orders of magnitude. We consider a plate made of Saint Venant-Kirchhoff type materials then we justify a new two-scale variational formulation. We assume that both the data and the displacement field admit a formal asymptotic expansion with a negative order of the leading term. We then prove that the lowest ordre term of the displacement field must be of order zero. Finaly, we consider the particular case of a laminated plate clamped along its lateral boundary and we how that tern satisfies a two-dimensional nonlinear membrane model.