A device for simultaneously supporting a tire which is to be recapped and for applying hermetically against the sidewalls of said tire a flexible sheathing which is connected to a source of vacuum comprises support means for supporting the tire by its beads and for varying the distance between the beads; annular means intended to be applied against the flexible sheathing in the region of the sidewalls of the tire; bearing means supporting both said support means and said annular means, said bearing means facing each other with an adjustable axial distance between them; and connecting means connecting said bearing means to each other and making it possible to vary the distance between said bearing means.