  In this paper we derive, by means of $\Gamma$-convergence, the periodically
wrinkled plate model starting from three dimensional nonlinear elasticity. We
assume that the thickness of the plate is $h^2$ and that the mid-surface of the
plate is given by $(x_1,x_2) \to (x_1,x_2,h^2\theta(\per))$, where $\theta$ is
$[0,1]^2$ periodic function. We also assume that the strain energy of the plate
has the order $h^8=(h^2)^4$, which corresponds to the F\"oppl-von K\'arm\'an
model in the case of the ordinary plate. The obtained model mixes the bending
part of the energy with the stretching part.
