A programmed computer control system provides on line predictive roll force gauge control and screwdown offset gauge control for a tandem hot steel strip mill. A gauge control program calculates corrective screwdown movement including that predictively required at each gauge controlled stand for optimum or near optimum gain correction of roll force error on the basis of on line detected roll force and screwdown position values at that stand and on the basis of a mill spring constant which is predetermined for that stand and a determined workpiece plasticity value for that stand. The workpiece plasticity values in determining the screwdown control action at each stand are adaptively modified during the workpiece rolling period on the basis of in process measurements of roll force and screwdown position at that stand. The control system operates the mill screwdowns in accordance with the program calculations made from the updated plasticity values.