Composite cap (1, 1') intended to be fastened to the glass ring (100, 100') of a bottle and then to serve as a stopper that can be screwed on and off as desired to close or open the pouring orifice of said bottle, said glass ring i) comprising in its upper portion an outer cylindrical wall (123, 123') with a diameter De and a ring top or lip (120, 120'); said lip comprising a top wall (121, 121') and an outer toroidal wall (122, 122'), with a radius R, serving as a transition between said top wall and said outer cylindrical wall; ii) being integral with an external screw thread (311, 130') and said composite cap comprising: a) a shell (10, 10'); b) an insert (20, 20') contained in said shell and rigidly connected to said shell, comprising a head provided with a lower face (23, 23'), and an internal skirt (21, 21') that is provided with an internal screw thread (22, 22') intended to cooperate with the external screw thread; c) a gasket, with an outer diameter Dj greater than De, having a peripheral annular portion comprising an axial compression zone, intended to come into contact with said lip, and an end border overlapping said top wall, said peripheral portion comprising a resilient layer with a thickness E, and being characterised in that: d) said insert comprises, at the junction between said lower face and the inner face of said internal skirt, a peripheral forming means associated with an oblique compression means which, during the pushing movement aimed at connecting said composite cap rigidly to said glass ring, act on said end border before the lower face of the head of the insert exerts axial compression on said axial compression zone, said forming means acting first on said end border, on which it exerts an annular bending stress, said oblique compression means acting second on a portion of said end border located in the vicinity of said axial compression zone. i) comprising in its upper portion an outer cylindrical wall (123, 123') with a diameter De and a ring top or lip (120, 120'); said lip comprising a top wall (121, 121') and an outer toroidal wall (122, 122'), with a radius R, serving as a transition between said top wall and said outer cylindrical wall; ii) being integral with an external screw thread (311, 130') and said composite cap comprising: a) a shell (10, 10'); b) an insert (20, 20') contained in said shell and rigidly connected to said shell, comprising a head provided with a lower face (23, 23'), and an internal skirt (21, 21') that is provided with an internal screw thread (22, 22') intended to cooperate with the external screw thread; c) a gasket, with an outer diameter Dj greater than De, having a peripheral annular portion comprising an axial compression zone, intended to come into contact with said lip, and an end border overlapping said top wall, said peripheral portion comprising a resilient layer with a thickness E, and being characterised in that: d) said insert comprises, at the junction between said lower face and the inner face of said internal skirt, a peripheral forming means associated with an oblique compression means which, during the pushing movement aimed at connecting said composite cap rigidly to said glass ring, act on said end border before the lower face of the head of the insert exerts axial compression on said axial compression zone, said forming means acting first on said end border, on which it exerts an annular bending stress, said oblique compression means acting second on a portion of said end border located in the vicinity of said axial compression zone. a) a shell (10, 10'); b) an insert (20, 20') contained in said shell and rigidly connected to said shell, comprising a head provided with a lower face (23, 23'), and an internal skirt (21, 21') that is provided with an internal screw thread (22, 22') intended to cooperate with the external screw thread; c) a gasket, with an outer diameter Dj greater than De, having a peripheral annular portion comprising an axial compression zone, intended to come into contact with said lip, and an end border overlapping said top wall, said peripheral portion comprising a resilient layer with a thickness E, and being characterised in that: d) said insert comprises, at the junction between said lower face and the inner face of said internal skirt, a peripheral forming means associated with an oblique compression means which, during the pushing movement aimed at connecting said composite cap rigidly to said glass ring, act on said end border before the lower face of the head of the insert exerts axial compression on said axial compression zone, said forming means acting first on said end border, on which it exerts an annular bending stress, said oblique compression means acting second on a portion of said end border located in the vicinity of said axial compression zone.