The invention relates to an installation and a method for producing glass stoppers which are provided with a head portion and are used for sealing wine bottles and sparkling wine bottles. Said installation comprises a mold for producing glass stoppers, a feeder system for supplying the mold with molten glass, a multistation press, and a removing and handling system for the finished glass stoppers. The mold is formed by a base that comprises a recess corresponding to a first partial length of the stopper, a central part consisting of two partial molding elements which can be displaced relative to each other as well as perpendicular to the longitudinal axis of the mold, can be coupled in a self-centering manner, and define a hollow space that corresponds to a second partial length of the stopper and to at least one main area of the head portion when said partial molding elements are coupled and rest against the base, and a top part which seals the hollow space of the head portion and is provided with a central male die that can be displaced in an axial direction relative to the top part so as to embody a recess in the head portion of the stopper, said recess compensating tolerances.