The invention concerns a device comprising: a packaging box for the flexible material part, dimensioned to hold said part flat; folding means for folding said part without direct handling; and a reception tube for receiving said folded flexible material part. The invention is characterized in that the folding means comprise; a traction suture connected to the flexible material part, which passes through the tube, and, walls forming a funnel whereof the base emerges proximate to the opening of the tube through which the flexible material part is designed to be inserted into said tube, said funnel being designed, when a traction is exerted on the traction suture, to gradually fold down the zones of the part located laterally relative to the tube towards the zone of the part located opposite the opening of said tube, to enable the part to be inserted into the tube.