When tightening a screw member with a nut runner, the turning angle of the screw member and the tightening torque of the same are detected. The ratio of increase in torque to increase in the tightening turning angle, that is, the torque increasing rate is calculated. Tightening of the screw member is terminated when the force imparted to the screw member exceeds the elastic limit of the screw member and reaches a predetermined tightening point in the plastic range. The total tightening turning angle and the final tightening torque are detected upon termination of the tightening. The elastic tightening turning angle portion of the total tightening turning angle is calculated on the basis of the final tightening torque and the torque increasing rate in the elastic range, and the plastic tightening turning angle portion of the total tightening turning angle portion is calculated by subtracting the elastic tightening turning angle portion from the total tightening turning angle. The plastic tightening turning angle portion thus obtained is compared with a preset tolerance range to evaluate the tightening.