There is provided a draping conveyor having a narrow upper margin, a flatwork piece feeding means for feeding sequentially flatwork pieces to a draping station, and flatwork piece engaging means for engaging the flatwork piece at the draping station and pushing a portion thereof over the top of the narrow margin of the conveyor as the feeding means continues to operate, so the flatwork piece is draped over the conveyor with a fold located on one side thereof and the confronting portions thereof extending from the fold depending and both exposed on the other side of the conveyor. The draping conveyor is moved first to a sewing station on the opposite sides of which sewing machines are positioned so operators can readily grasp the exposed end portions of the flatwork piece delivered thereto and apply the same to their sewing machines simultaneously. The flatwork pieces fed sequentially to the draping station are formed from the unwound portion of a roll of flatwork piece forming material which is carried by said feeding means past a severance station. The feeding means is momentarily stopped to allow a severing means to move across the flatwork piece forming material to sever a flatwork piece from the end of the unwound portion of the roll of such material.