Abstract: A 4-high-rolling mill includes a pair of upper and lower works, a pair of upper and lower backup rolls supporting the upper and lower work rolls, respectively, a roll bending device for applying a bending force to the upper and lower work rolls, and a roll shift device for shifting the upper and lower work rolls in an axial direction of the work rolls. Each of the upper and lower work rolls has a curved initial crown portion formed on one side portion of a barrel of the work roll which is not less than a half of the length of the work roll barrel, and a substantially cylindrical initial crown portion formed on the remainder of the work roll barrel. Teh curve of the curved initial crown portion approximates to a curve represented by the formula Y=X.sup.n, (n.gtoreq.1.