To provide a vibration damping device capable of achieving the stable movement and a punch laser composite machine unaffected by the vibration during the punching.

A conical portion 27 of a shaft 29 is fitted to a first housing 41 to position the shaft 29 by relatively moving the shaft 29 to the first housing 41 and a second housing 43 by a moving means 57, and the other end thereof is clamped and fixed by the second housing 43. When unclamping the shaft 29, the shaft 29 is moved in the opposite direction by the moving means 57, and the shaft 29 is supported via a vibration damping material 53.