A cooling bed for rolled material has a single driving shaft from which the vertical and the horizontal movements of a first support grating relatively to a second support grating are derived. The driving shaft carries a first group of control discs with control cams for effecting the vertical movement and a further group of control discs with control cams for effecting the horizontal movement of the first support grating the control cams permitting the movement processes to be so controlled that the rolled material is extremely carefully treated during the transverse conveyance thereof.