Abstract: The device includes two rolls (10, 11) held by bearings (13, 14) on a frame (16) and, for each roll, devices (22) for measuring the position of the generatrix diametrically opposite the neck between the rolls, at three or more points lying respectively in a mid-plane (P.sub.3) perpendicular to the axes and in secondary planes such as (P1, P5) parallel to the mid-plane, and means (23) for measuring, in the said mid-plane, the position of a generatrix lying at 90.degree. to the neck. The method according to the invention uses these measurements to determine continuously the gap between the rolls, taking into account the in-service deformations of the rolls.