A process for mounting an outer bearing ring involves press fitting a stamp into the outer ring so that the inner peripheral surface of the outer ring assumes the shape of the stamp. Using the stamp, the outer ring is then press fitted into the recess of a machine part so that the contour of the external peripheral surface of the outer ring is plastically molded through axial stretching into the machine part. To mount an inner ring, a stamp with a bore is press fitted onto the inner ring so that the inner peripheral surface of the inner ring pressing against the stamp assumes the shape of the bore of the stamp. Using the stamp, the inner ring is then press fitted onto the machine part and the contour of the inner peripheral surface of the inner ring is plastically molded through axial flow forming into the machine part.