Abstract: A method and apparatus for continuous cold cutting or slitting of a flat material wherein the flat material is subjected to a first step of partial-shearing or penetration in a zigzag state to a controlled depth of penetration, and subsequently to a second step of flattening, thus forcing the penetration formed in the material back to substantially the original thickness of the material, thereby to perform complete severing or slitting the material having no burrs formed during the operation. The first working action is obtained from feeding of the flat material into the controlled spacing of opposing pairs of cutter discs so that there occurs partially shearing or penetration in the flat material under an optimally predetermined interfering action by the opposing pairs of cutter discs into the material when it engages therewith.