A tool for supporting multilayer printed circuit boards during manufacture having a frame in which there is fixed a pretensed, non-electrically conductive fabric which has a thickness less than 0.1 mm and which can be accessed by its two faces. The tool allows the induction bonding of the layers at internal points of the bundle following a method in which the bundle is placed on the tool and at least one of the welding electrodes used in the welding operation is applied on the lower face of a fabric of the tool supporting the bundle. A machine especially suitable for putting the method into practice includes C-shaped magnetic cores, the arms of which are long enough to reach the internal points of the bundle.