In a vibration damper of a turbomolecular vacuum pump, a vacuum tightness function and a vibration damping function are both performed by one or more toroidal rings made of an elastic material. The elastic rings assume a resting configuration while the vacuum pump is not operating and the damper is at atmospheric pressure, and they assume a compressed configuration while the vacuum pump is operating and the damper is under vacuum conditions. In the compressed configuration, the elastic rings are deformed due to a compression force. This deformation of the elastic rings prevents metal-to-metal contact between the vacuum pump and a vacuum chamber to which the pump is connected through the damper.