The natural vibrations of the infinite rectangular plate, strengthened by the periodically located transverse identical stiffening ribs, prepared of another more durable material are investigated. The optimum geometric parameters of construction are determined, which ensure the greatest value of the lowest frequency of the natural vibrations, with its fixed weight. For the comparison also the cases are investigated, when ribs are substituted by equal with them by the weight lower layer, or identical outer layers of plate. It shows that the greatest value of the lowest frequency of the natural vibrations is possible to reach in the case of strengthening the plate by stiffening ribs.