An arrangement of attenuating the vibration in a roll assembly of a fiber web machine, in which assembly the roll (10) being rotatably suspended at its end on bearings in bearing housings (13a, 13b), and the bearing housings being supported on the frame or the foundation of the machine via viscoelastic intermediate piece or pieces (21a, 21b). The loss factor of the intermediate piece is greater than 0.1 at the normal operating conditions of the roll at a frequency range, which is ±10% calculated from the lowest bending eigenfrequency of the roll, and in the each end of the roll the spring constant of the total influence of the intermediate piece or pieces is in the range of 0.04 GN/m-1 GN/m.