In a state where the expanded protruding portion of the heat-exchanging tube, which has been expanded inside a grip portion of a chucking sleeve whose diameter has been reduced by a clamp bushing, is gripped by the grip portion, a tube expanding billet is inserted into a yet-unexpanded part of the heat-exchanging tube to cause tube expansion. When doing so, a guide portion, which is formed on a flare punch and has the same diameter as the maximum outer diameter of the tube expanding billet, is inserted inside the expanded protruding portion of the heat-exchanging tube gripped by the grip portion.