A container (1) has an applicator cap (2) for a cosmetic product and a flexible tube (3) having a skirt (31) and a tube head (32) having a shoulder part (321) and a neck (322) with an opening (3221), The tube head (32) is connected to the skirt (31) by the shoulder part (321). The flexible tube (3) acting as a reservoir to contain some cosmetic product. The applicator cap (2has a base (21) and an applicator, the base (21) being designed to fix onto the tube head (32) and plug the opening (3221) and the applicator being fixed to the base (21) so as to be housed inside the flexible tube (3) when the base (21) is fixed to the tube head (32) and plugs the opening (3221). The skirt (2) is made of a multilayered plastics material (4) comprising at least one barrier layer (41).