To provide a cylindrical vibration control device of novel structure, in which a pair of right and left stopper rubber plate can be accurately assembled by specifying circumferential positions and both sides of them, and a trouble caused by wrong assembly can be avoided with simple structure.

Engagement recess parts 58 or engagement projection parts 40 are formed at mutually and circumferentially corresponding three or more positions with respect to an inner circumferential face of a mounting hole of each stopper rubber plate 20 and outer circumferential faces of both ends of an inner shaft member 12 which is inserted into the mounting hole. Since the engagement recess parts 58 or engagement projection parts 40 have at least three variations in circumferential spaced distance, a pair of the same stopper rubber plates 20, 20 mounted on axial both sides can be assembled by specifying both sides of them and the circumferential directions around the inner shaft member 12.