A tire holding device of a tire mounting machine grasps the bead section of a green tire by chucking paddles and places the green tire around an upright cylindrical vulcanization bladder. A bladder device of the tire mounting machine expands the vulcanization bladder to press same against the inner surface of the green tire, and sets the green tire in a vulcanization-mold. On a lower portion of each chucking paddle, guide extensions are formed to extend in the two circumferential directions. Between adjacent chucking paddles, the guide extensions extend toward each other and constantly overlap each other to prevent the expanding vulcanization bladder from contacting the radially inner surface of the bead section and from stripping the non-vulcanized rubber of the green tire.