A method of mounting a semiconductor chip part on a substrate, which is capable of realizing high efficiency and high reliability of the mounting works. A leading end of a conductive wire is contact-bonded onto each pad of a semiconductor chip part, followed by tearing of the wire, to form a two-step bump having an upper step portion and a lower step portion larger in volume than the upper step portion. Only the upper step portions of the bumps are then brought in press-contact with a single flattening tool member having a flat surface in such a manner that heights of all of the bumps are made nearly equal to each other. A conductive paste is stuck on the bumps, and the substrate is coated with an adhesive. Thus, the semiconductor chip part is heated and pressurized onto the substrate by a mounting tool in such a state in which the pads are aligned with the corresponding lands of the substrate, to plastically deform the whole of the upper step portions and the lower step portions of the bumps.