PURPOSE: To elevate the accuracy matching of the length of a periphery by overlapping an endless belt like elemental body in the thickness direction and by performing an age heat treatment with fitting to the mandrel consisting of the material having larger thermal expansion coefficient than that of the stock.

CONSTITUTION: A thin tubular body is made by welding from the band of 18% Ni marageing steel, etc. and the stock for belt elemental body is obtd. with cutting into round slices. A belt elemental body 1 is formed with performing the rolling in peripheral direction of the stock so as to make the plural stages of the prescribed size by the small sized rolling mill 3 having an idler 2. An age heat treatment is then performed with overlapping in the thickness direction the stock 1 having a stepwise diameter size difference to the mandrel consisting of the material having larger thermal expension coefficient than the belt elemental body 1. Because of the precipitation reaction at the age heat treatment being performed at the stress factor in the peripheral direction the stress is made a fixed value. Consequently the tension load is equalized and peripheral length matching accuracy is elevated.