Abstract: A damping device is constituted by a substantially cylindrical damper body (1) with an axial through bore (6), where the bore (6) accomodates a central pipe (3) which e.g. can lead a cooling liquid. The central pipe (3) is connected rigidly to or into the machine element to be damped, preferably in a cylindrical and axial cavity in a boring bar (9). Ring-shaped, elastic spring elements (2) placed in the ends of the damper body (1) and between the central pipe (3) and the damper body (1), as well as damping oil (4) in the clearance between the central pipe (3) and the damper body (1) transform motion energy into heat and provide the damping action. The stiffness of the spring elements (2) can optionally be adjusted.