PURPOSE: To perform caulking with high quality by caulking a mantle tube onto a cap with an initial bending part to bend the mantle tube into a small caukening angle and a press die to bend it along the cap's surface shape in a final caulking angle.

CONSTITUTION: In a 1st process with a press die 1, an initial bending part initially bends an opening end's neighborhood of the mantle tube (a 1st member) A only by a 1st angle smaller than a prescribed final caulking angle facing toward an outer peripheral surface of a cap (a 2nd member). In a 2nd process, following the opening end of the mantle tube A along the surface shape of the outer peripheral surface of the cap C, it bends until the final caulking angle. Just after this operation a spring back preventing projecting part bends the opening end of the mantle tube A following along the peripheral shape of the cap C into a R like, and closely sticks the opening end of the outer tube A on the upper surface of the cap C. In such a way, in the final tightening angle, pressing is forcibly executed without generating a clearance or an agnail, etc., on the tightening part, a gap following to tightening does not generate, and the beautiful sight is also not spoiled.