A system (22) for absorbing bending vibration in a shaft (24) which is drivingly rotated about an axis (26) and wherein the shaft is exposed to bending disturbances utilizes a body (30) attachable to the shaft for rotating therewith as the shaft rotates about its axis of rotation and round roller elements (44) positioned within cavities (40) disposed in the body. During operation of the system, the bending disturbances induce pendulum-like motion of the roller elements within the cavities in a manner which absorbs bending vibration of the shaft. The roller elements, the cavities and the bending disturbances are related to one another in accordance with an equation which optimizes performance of the system and circumvents time-consuming trial and error techniques during design of the system. In the event that the cavities have spherical walls and the roller elements are spherical in form, the system is capable of absorbing torsional, as well as bending, vibrations in a rotating shaft.