Abstract: The invention related to a device for layer-stacking web-like materials, comprising a fixed table on which a carriage is mounted for sliding, said carriage supporting a roll of material mounted for free rotation on a support and being held by pressure against at least one endless driving elastic belt mounted on two rollers placed in parallel relationship inside a vertical plane, said rollers being driven in rotation by a position- and speed-controllable driving member, the material being unrolled and going down freely vertically in order to be laid on the laying table.