The invention relates to a method for producing a vessel closure for vessels comprising an opening that is to be closed by the vessel closure, an inner diameter of more than two cm and surrounds a polymer-based sealing element that is arranged in the vessel closure in such a manner that is sealingly rests on the opening of the vessel in the closed state. A polymer material becomes sufficiently free-flowing by warming and is applied to the vessel closure in the region of the sealing element that is to be produced, and optionally, is mechanically formed into the desired shape which it maintainsafter cooling. The invention also relates to a metal or plastic vessel closures for vessels for receiving drinks or food, and comprises a sealing insert, the material thereof being selected so that the migration of material components into the drink or food, that are a health risk, is prevented. The invention also relates to corresponding materials for said type of sealing inserts and to the use of specific polymers for producing the above-mentioned sealing inserts.