To provide an elastic connecting device for a shock absorber which connecting device does not pose the problem that water pools in a metal fixture for fixing a shock absorber to a vehicle body to cause rust to grow on a piston rod or the metal fixture.

According to the elastic connecting device, the piston rod 14 of the shock absorber 10 is connected to the body 18 via a lower cushion rubber 26, using the metal fixture 16. A mounting plate 22 for the metal fixture 16 is provided with a drain hole 80 penetrating the mounting plate 22 vertically. A bound stopper 44 is provided with a peripheral groove 82 on the upper face of the bound stopper 44, where the groove 82 is located in correspondence to the drain hole 80 and a radial groove 84 is formed to be continuous with the peripheral groove 82. The grooves 82, 84 allow water from the drain hole 80 to drain out so as to prevent infiltrating water from pooling in a cuplike first holding part 40 of the metal fixture 16.