We are interested in the study of a thin plate, periodicially perforated by cylindrical holes, the axes of which are perpendicular to the plane of the plate. A horizontal section of the plate specifies its geometry, and shows a periodicity in the order of E. The thickness of the plate is equal to e. The ratio of material is small, and is characterized by the parameter 6, the thickness of the bars being equal to ~6. In this paper, we study the dependence of displacements on e, E and 6, and to give equivalent limits when e, then E, and finally 6, tend towards zero. An interesting result obtained in this work is the negative Poisson coefficient of the final equivalent material. Although this coefficient is theoretically between - $ and 1, most materials encoun- tered in practice have a positive one.