PURPOSE: To relieve the residual stress of a cylindrical welded structure by simultaneously heating the outsides of structure parts apart from a heating chamber to make a temp. gradient gentle in local annealing of the structure by an internally heating method.

CONSTITUTION: In local annealing of weld zone 3 between lower barrel 1 and upper barrel 2 of a cylindrical welded structure, both sides of zone 3 are partitioned with partition walls 6, 7, and inner heating elements 4 are set to form a heating chamber. On the other hand, the outsides of barrels 1, 2 are provided with outer heating elements 9 at positions apart from the chamber and covered with heat insulating material 5a. Zone 3 is annealed by being simultaneously heated with elements 4, 9.