The invention relates to a device for rolling, in particular for stepped rolling, of rolling stock with at least one pair of rolls and at least one linear drive arranged downstream of the pair of rolls in the rolling direction, which together with the pair of rolls can apply tensile stress to the rolling stock, and with means for detecting the tensile stress. In order to enable an improved method of flexibly rolling stock, the rolling device is characterized by means for detecting the tensile stress and by a control device for controlling the drive power of the linear drive as a function of the tensile stress detected, in order optionally to vary the tensile stress applied to the stock or to keep the tensile stress constant as the drive speeds behind the roll gap change. The invention also relates to a method of rolling the rolling stock using such a device.