The invention relates to rolls of a skewed-roll machine. The rolls include a back-up roll and a pressure roll, having their axes extending at an angle to each other and at an angle to the trueing axis. The back-up roll has a biconcave profile, the portions of this roll, adjoining its ends, having the same hyperboloidal concavity with the degree of curvature providing for the engagement of the roll with the narrow central portion of the article being trued. The central portion of the back-up roll has hyperboloidal concavity with a degree of curvature to perform the trueing by bending the thickened end portion of the article being trued. The other roll, i.e. the pressure one, has a convexo-concave profile with similar hyperboloidal concave portions adjoining its ends, providing for the engagement of the roll with the thickened end of the article being trued, the roll further having a convex central portion as a projecting strip of a curvilinear profile, with a radial projection having a height ensuring a bending torque which, at the bending of the narrow central portion of the article being trued is short of the maximum permissible value of the bending torque but is not short of the minimum permissible bending torque required for trueing the thickened end of the article being trued, provided that the plastic torque of the bending resistance of the cross-section of the thickened end portion of the article being trued exceeds the plastic torque of the bending resistance of the cross-section of the narrow portion by not more than 10%.