To improve the quality of a ribbon-shaped rubber material and a rubber member formed from the ribbon-shaped rubber material by making the cutting shape of the ribbon-shaped rubber material molded by a rubber molding machine uniform.

The ribbon-shaped rubber material 5 is molded continuously by extruding rubber from the opening 13B of the mouthpiece 13 of the rubber molding machine, wound onto a rotating support, and laminated to form the rubber member. Simultaneously with the completion of rubber member forming, the molding of the ribbon-shaped rubber material 5 is stopped, and the ribbon-shaped rubber material 5 is cut by the cutting means 31 of a cutting device 30. When cutting, the cutting means 31 is moved from a standby position by a moving means to cross the opening 13B while the opening plane 13A of the mouthpiece 13 is slid, and the ribbon-shaped rubber material 5 is cut along the opening plane 13A by a cutting blade 31A. After that, the cutting means 31 is separated from the opening plane 13A and moved reversely while being prevented from contacting the cutting end of the ribbon-shaped rubber material 5 to the original standby position.