A controlled deflection roll possesses a roll shell which is radially movable in at least one plane in relation to a roll support. Position feelers or sensors are arranged at the ends of the roll shell. These position feelers control regulators operatively associated with pressure or support elements located between the roll support and the roll shell, as a function of deviations from a predetermined reference or set position, in a manner such that the roll shell is maintained in the reference or set position. It is possible to influence the pressure or support elements by the position feelers either equally or unequally, and specifically, with decreasing intensity in the presence of increasing distance from the related position feeler.