A rolling mill has a work roll (1), a back-up roll (2) for supporting the work roll (1) vertically and driving it. A plurality of horizontal support rollers (4,6) contact the work roll at barrel diameter outside the rolling region and at both horizontal sides of the work roll and act to fix the position of the work roll in both horizontal directions during rolling and to oppose horizontal rolling forces. In order to reduce the bending of the work roll during rolling, there are provided means for applying horizontal counterbending forces to the work roll comprising members (5,7) e.g. rollers, contacting the work roll at locations axially further from the rolling region than the support rollers (4,6) and actuator means (14) for urging the members (5,7) against the work roll. The counterbending forces being in the same direction as the net horizontal force applied to said work roll by said back-up roll and the material being rolled. Preferably at least one condition of said work roll is sensed during rolling, and there are control means acting during rolling to control the counterbending forces in dependence on the sensed condition.