To provide a connection device having a higher degree of flexibility in design for connecting one of a cylinder and a piston rod of a shock absorber to a vehicle body in a state of permitting the relative movement to the vehicle body.

The connection device includes a connection device body 40, a movable member 42 axially movable relative to the connection device body 40, and a connection rubber 76 for connecting the connection device body to the movable member while permitting the relative axial movement. The connection rubber 76 consists of a body rubber portion 70, a bound stopper rubber portion 72, and a rebound stopper rubber portion 74, separately from one another. The bound stopper rubber portion 72 is provided between an end wall 48 of the connection device body 40 and a stopper plate 54 inside the connection device body, and the rebound stopper rubber portion is provided between the end wall 48 and a stopper plate 56 outside the connection device body 40.