A rod acceleration reducing mechanism is provided in a bottom-side oil chamber in an inner tube. The rod acceleration reducing mechanism includes a housing having a cylindrical accommodating casing screwed onto a fastening bolt of a bottom valve and a cap, a free piston displaceably fitted in the housing to define variable chambers at vertically opposite sides thereof, and elastic disks applying an elastic resistance to the displacement of the free piston. The variable chambers formed in the housing are variable in volume in response to pressure changes in the bottom-side oil chamber and the reservoir chamber. Thus, rod vibration can be generated by the rod acceleration reducing mechanism to reduce generation of rapping noise during running of the vehicle.