A fin member for a heat exchanger is produced by repeatedly folding a plate over itself into a corrugated shape to form corrugated fins. The folded sections which are formed by the folding are pressed and deformed into a recessed shape to form engagement recesses. A pipe member through which fluid flows is disposed at the engagement recesses. The pressing and deformation of the engagement recesses cause swollen sections to protrude at both sides of each folded section with respect to the folding-over direction of the folded section and form flat butt surfaces at the tips of the swollen sections. Adjacent butt surfaces are caused to be in surface contact with each other with the pipe member disposed at the engagement recesses.