The backing device has a back-up roll placed between the housings of a roll stand and the ends of the roll are mounted in the guide windows of the housings. A hydrostatic bearing has a body which rests on the back-up roll and a shell whose internal surface is spaced by a clearance from the barrel of the back-up roll and is provided with pockets. The back-up roll rests by its ends on a supporting beam which is pressed against it by pressure screws. The bearing shell is urged against the roll barrel by hydraulic cylinders mounted between the supporting beam and the bearing body. The chambers of the hydraulic cylinders are connected through respective conduits and throttles to the pockets on the shell internal surface, and there is at least one pocket for each hydraulic cylinder. The pockets and the respective hydraulic cylinders are connected to a single source of fluid under pressure.