A vehicle wheel bearing apparatus which limits hoop stress generated in the inner ring during caulking, to below a predetermined level, can improve durability and reliability of the inner ring. Radial expansion of the outer circumferential surface of the inner ring, before and after said plastic deformation, is measured so that the amount of radial expansion of the inner ring is controlled based on a predetermined relationship between the hoop stress and the amount of radial expansion of the inner ring. The hoop stress in the inner member is limited below a predetermined level. Thus, it is possible to easily and exactly control the hoop stress in the inner ring caulked onto the hub. This prevents the generation of cracking or delayed fracture of the inner ring, to provide a bearing apparatus with an inner ring with superior durability and reliability.