Abstract: A device for stacking pieces of fabric which includes a fold bar, at least one gripper movable in translation for grasping succesive pieces of fabric on the fold bar, a fold bar support which is movable between a rear position and a front position for receiving the pieces of fabric from the outlet of a sewing machine, a stacking table positioned adjacent to the fold bar, the gripper being driven in an alternating motion between a position in which it is located over the fold bar support when the support is in its rear position, and a position in which it is located over the stacking table and a guide bar which faces the stacking table at a level which is higher than the greatest possible height to which the fabric can be stacked.