A packaging method for packaging elastomer parts (1), such as stoppers for pharmaceutical containers, the method comprising the following steps:packaging parts (1) in a primary bag (10) made of material that is substantially impermeable to gas； andintroducing in said primary bag (10), a nitrogen-based atmosphere, with at least 80% nitrogen； said primary bag (10) being packaged in a secondary bag (20), with a vacuum being applied between said primary bag (10) and said secondary bag (20)
