A roll, as in a paper making machine press section, with vibration damping, wherein the roll includes a stationary central shaft, a rotatable annular, roll shell, a plurality of hydraulic pressure chambers each with a shoe hydraulically supported therein and pressed against the interior of the annular roll shell, wherein the roll shell is subject to vibration, which vibrates the support elements. A hydraulic pressure liquid feed channel extends through the stationary shaft and communicates with each pressure chamber. A respective throttle in the form of a channel either between the feed channel and each of the pressure chambers, or one throttle channel communicating with several of the pressure chambers or a throttle channel communicating into the feed channel from the source of pressure fluid. The cross section of flow through the throttle channel is selected according to a formula, typically wherein the product d.sup.2 .times.n.sup.-1 is between 6 mm.sup.2 and 90 mm.sup.2 where d is the cross section of a throttle channel and n is the number of pressure chambers supplied by the respective throttle.