The invention relates to a tool for supporting multilayer printed circuit boards during manufacture comprising a frame in which there is fixed a pretensed, non-electrically conductive fabric which has a thickness less than 0.1 mm and can be accessed by its two faces. The present tool allows the induction bonding of the mentioned layers at internal points of the bundle following a method in which said bundle is placed on the tool of the invention 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 comprises C-shaped magnetic cores the arms of which are long enough to reach the internal points of the bundle.