A steel tube hot-finished by the Mannesmann tube-making method is subjected to a simple grinding process for the inner surface, and thereafter to a cold drawing, so that the depth d of the concave portion in the concavo-convex profile forming the inner surface of the steel tube, the surface roughness Ra and the width w of the entrance in the concave portion are specified, or similarly the depth d of the concave portion in the concavo-convex profile, the Vickers hardness Hv of the inner surface layer and the width w of the entrance in the concave portion are specified, hollow parts for a drive shaft, which have an excellent fatigue strength and which is optimal to reduce the weight of a car body, can be produced. Accordingly, the application of the manufacturing method according to the present invention allows drive shafts for automobiles to be efficiently produced in a reduced manufacturing cost, thereby providing a significant advantage in the industry.