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In this paper we derive, by means of $\Gamma$-convergence, the periodicallywrinkled plate model starting from three dimensional nonlinear elasticity. Weassume that the thickness of the plate is $h^2$ and that the mid-surface of theplate 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 platehas the order $h^8=(h^2)^4$, which corresponds to the F\"oppl-von K\'arm\'anmodel in the case of the ordinary plate. The obtained model mixes the bendingpart of the energy with the stretching part.

Periodically wrinkled plate of the F\"oppl-von K\'arm\'an type