Herein disclosed are outer race working method and apparatus of the type, in which such a roughly shaped outer race workpiece of a Birfield type constant-velocity ball joint as is formed with a groove made axially straight at its portion above the joint center and having an axial curvature below the joint center, in which a hexagonal-pillar guide punch and a split mandrel composed of six segments are inserted into the aforementioned groove of the roughly shaped workpiece thereby to iron the inner surface of the aforementioned groove and to form both a center hole corresponding to the center of a ball rolling groove and a face for providing a reference for the axial position of the groove center, and in which the roughly shaped workpiece is then ironed by means of an ironing die, whereby the ball rolling groove is plastically worked all over its surface from its lower portion to its upper portion.