To suppress a remarkable waste of materials by welding both free end sections of a member of a ring-form material made of steel together in such a manner that the member of the ring-form material made of steel of a specified length may be formed into a shape of a box shape ring member made of a ring-form steel.

In the production or the manufacture of an annular ring member 112, a tubular material of an approx. rectangular or square shape, which is already cut by a specified length in the axial direction being required for the production or manufacture of the annular ring member 112, is attached in a proper attaching tool, and bent into a circular shape. Then, both free end sections of the annular material are welded together so that the annular ring member 112 may be formed. By this constitution, the annular ring member 112 can be produced or manufactured from a raw material in such a manner that the excessive waste of the material is almost eliminated. In addition, by using the tubular material, the weight of the annular ring member 112 can be drastically reduced.