Abstract: In a variable crown sleeve roll, the inner peripheral surface of a sleeve is sealingly secured at opposite ends to the opposite ends of the outer peripheral surface of an arbor to define a chamber of a predetermined shape therebetween in the central portion of the sleeve. A pressurized fluid is supplied to said chamber through a passage in the arbor to distend the sleeve so as to control the amount of the crown of the roll. Values of the smallest thickness of the sleeve at the axially central part of the sleeve, the length of the pressure receiving part of the sleeve and the sleeve thickness taper angle for defining said chamber are selected in accordance with predetermined conditions.