Abstract: Vibration damping apparatus (40) includes a body in the form of backup roll balance piston (42) positionable for sliding movement in an enclosure in the form of cavity (44) in the lower backup roll chock (30) of the mill stack (10). The body of the piston is a casing which performs the role of a conventional postion. A damping means is integral with the piston (42) for providing vibration damping of opposing backup roll chocks (24, 30). The damping means is a specially designed absorption system to provide tuned stiffness and damping elements which act in parallel and are located in compartment (46) at an uppermost end or cap of the piston (42). A second vibration absorbent compartment portion (56) of the piston (42) also includes vibration absorbing components. Portion (56) is an integral cap located at the end of the piston (42) in contact with the fluid (52).