A hollow shaft, which is usable with a constant velocity universal joint, has an increased static torsional strength and torsional fatigue strength of a small diameter portion (small diameter portion having a smooth outer peripheral surface) formed near a spline at an end portion of the hollow shaft, and has a reduced manufacturing cost. The hollow shaft is molded by plastic working from a tubular blank, and subjected to quench hardening treatment. The quench hardening treatment includes carburizing and quenching treatment. The hollow shaft includes a softened section formed in a part of the hollow shaft by local heating treatment after carrying out the carburizing and quenching treatment.