The present invention relates to a closing part (1) for beverage containers, which includes a generally tubular cover (3) made of a food-grade sealing elastomer material. A first end is closed by an end portion (5) in which an opening (51) for dispensing the beverage is provided. The second end (41) of the cover (3) is arranged such as to be connected to a container. Near said second end (41), the cover (3) has a portion (43) which is flared in the direction of the second end (41). The shape of said flared portion (43) and the constitutive material thereof, along with the thicknesses and elastic characteristics thereof, are determined together in order to allow for a plurality of elastic deformation ranges or the flared portion (43) depending on which portion thereof is deformed in a state of connection to a container. The closing part sealingly fits onto an assortment or containers having different sizes.
