Abstract: A web punched by a fin press and continuously fed therefrom is intermittently fed by increments equal to a desired number of tiers of punched holes in the web into a space below a pressure plate. The web is then held under suction by the pressure plate and cut off by a cutter into a plate fin. The pressure plate with the cut-off plate fin held thereby is horizontally fed along an interval in the direction in which the web is fed. The plate fin then is released from the pressure plate so as to drop onto a mobile carriage below the pressure plate until hairpin pipes carried by the mobile carriage in upstanding disposition are inserted through the punched holes in the plate fin. The pressure plate moves back to its original position. The above cycle of operation is repeated until a prescribed number of plate fins are fitted over the hairpin pipes. Thereafter, the pressure plate is lowered to depress the plate fins for thereby stacking the plate fins on the hairpin pipes.