A beverage container comprises a body for receiving fluids, having a base, a first side wall adjoining the base, and an opening section adjoining the first side wall and having a discharge opening. The container further comprises a cover module that is placed on or is present on the body and has a second side wall and a cover flap adjacent thereto. When the cover module is present on the body, the first and the second side walls form an outline shape of the container, at least in sections, the diameter of which has at least one maximum. At least one film, at least in regions, rests on the first and second side walls, and extends on one side and an opposite side at the body at the at least one diameter maximum. The film may be a shrink film that is shrunk on the first and second side walls.