Abstract: The invention provides a pinning table for fabric stacks of the type including:an upper fixed platen provided with openings, and intended to receive the fabric;a lower movable platen, parallel to the upper platen;a plurality of pins adapted to be introduced into said holes in the upper platen, and connected to said lower platen; andmeans for imparting a translational movement to the lower platen with respect to the fixed upper platen, in a direction perpendicular to said platens, wherein said lower platen is formed from at least a first and second superimposed plates each having a plurality of orifices arranged identically and corresponding to the openings in said upper platen, and in which the pins are introduced, at least one of said plates being slidable, in a limited way, with respect to the other plate through actuating means.