Abstract: The process according to the invention relates to the packaging of lids cut out in a press combined with a stacker. According to the process, the guide rods of a delivery magazine are covered by a substantially cylindrical casing which simultaneously surrounds the stacked lids while at the same time immobilizing the stack transversely to itself with a slight clearance therebetween, the casing comprising support means for resting on the moving supports at the bottom of the stack of lids and stop means for retaining the bottom of the stack borne by the casing. The retaining means are optionally completed by one or more associated retaining means. The stack of lids covered in this way is then removed from the delivery magazine and the casing is sealed with caps which offer an added measure of protection.