Although the conventional continuous riveting machine was able to use exclusively a special blind rivet having a longer core-stem than that of the standard type, the continuous riveting machine according to the present invention is able to use the standard blind rivet and also able to recover separately torn core rivet stems and a blind rivet-holding belt made of plastic material enabling the supply of blind rivets in series. When a lower piston 600 descends in a jaw cylinder 400, a nose piece 620 integrated in one piece with the lower piston 600 also descends while bending downwardly plastic upper and lower tabs of the blind rivet-holding belt, and holding the blind rivet. Torn-core-stems are absorbed and stored in a torn core rivet stems storing case installed on the upper portion of the jaw cylinder by applying vacuum air absorbing force generated in a vacuum ejector.