To complement defect of a shock absorber itself having low vibration suppression capability in a fine displacement zone and to improve riding comfort by suppressing vibration of a vehicle body and the like.

A mounting tool 1 has a first mounting metal 2 with a first rubber mounting face 2S and interlocking to an end e1 of the shock absorber C, a second mounting metal 3 with a second rubber mounting face 3S and interlocking to a supporting member F1 and a vibration suppression rubber member 4 fixed to the first and second rubber mounting faces 2S, 3S and a spring means 5 for returning the first and the second mounting metal 2, 3 to their initial position Y0. The rubber stiffness of the vibration suppression rubber member is 65±10. In the vibration suppression rubber member, rubber stiffness is 65±10°, loss tangent is 0.55±0.1, tensile strength is equal to or larger than 4Mpa, and elongation at the time of fracture is equal to or larger than 650%.