A bush bearing with a radial stiffness that changes in the circumferential direction. The bearing has at least one radial web with a high radial stiffness in a first radial major load-bearing direction, and at least one pocket with a significantly smaller radial stiffness than in the region of the radial web in a second radial direction which is preferably perpendicular to the first radial direction. To achieve a large force-displacement ratio and simultaneously a soft torsion characteristic, the inner element of the bearing of the invention is formed in two parts. It consists of a metal inner sleeve and a preferably also metal bearing core received in the inner sleeve. An elastomer or a rubber contour is vulcanized on the inner surface of the inner sleeve or the outer surface of the bearing core. The inner core is oversized with respect to the inner diameter of the elastomer contour. The bearing core is pressed into the inner sleeve, but does not adhere to it.