A method for the laser-based machining of a sheet-like substrate, in order to separate the substrate into multiple portions, in which the laser beam of a laser for machining the substrate is directed onto the latter, is characterized in that, with an optical arrangement positioned in the path of rays of the laser, an extended laser beam focal line, seen along the direction of the beam, is formed on the beam output side of the optical arrangement from the laser beam directed onto the latter, the substrate being positioned in relation to the laser beam focal line such that an induced absorption is produced in the material of the substrate in the interior of the substrate along an extended portion, seen in the direction of the beam, of the laser beam focal line, such that a material modification takes place in the material of the substrate along this extended portion.