The method comprises forming a beam (2a) of a laser device (3) irradiated on an outside of an optical arrangement along a direction of an expanded laser beam focal line, and directing the laser beam towards a to-be processed substrate. The optical arrangement is positioned in a beam path of the laser. The substrate is positioned relative to the laser beam focal line so that: the laser beam focal line generates an induced absorption in a material of the substrate along a beam direction extended portion for generating cracks in the material of the substrate by the extended portion. The method comprises forming a beam (2a) of a laser device (3) irradiated on an outside of an optical arrangement along a direction of an expanded laser beam focal line, and directing the laser beam towards a to-be processed substrate. The optical arrangement is positioned in a beam path of the laser device. The substrate is positioned relative to the laser beam focal line, such that: the laser beam focal line generates an induced absorption in a material of the substrate along a beam direction extended portion for generating cracks in the material of the substrate by the extended portion; and the extended portion extends to two opposite substrate surfaces. The extended portion further extends over more than 90% of a thickness of the substrate. The cracks are generated without removing and melting the material of the substrate. The extended portion and/or the laser beam focal line extends 0.3-10 mm into an interior of the substrate along a beam lengthwise direction. The thickness of the substrate measured perpendicular to the two opposing substrate surfaces is 100-1000 mu m. A ratio to the extent of the extended portion and/or the laser beam focal line to the thickness of the substrate is 2-5. A ratio of a dimension of the extended portion and to an average extent of the extended portion is 50-500. A spot diameter of the laser beam focal line is 1-2 mu m. A pulse duration of the laser device is selected such that a heat diffusion is carried out at the time of interaction with the material of the substrate and if no heat diffusion is carried out, the pulse duration is 100 ps. A pulse repetition frequency of the laser device is 100 kHz. The laser device is operated as a single pulse laser device or a Burst mode laser device. An average laser power measured directly on the output side of the laser beam is 30-50 W. A wavelength of the laser device is selected such that the material of the substrate is transparent to the wavelength and an intensity of the laser beam decreases to = 10% in the material of the substrate. If the laser is neodymium-doped yttrium aluminum garnet, yttrium-doped yttrium aluminum garnet and erbium-doped yttrium aluminum garnet, the wavelength of the laser beam is 1064 nm, 1030 nm and 1.5-1.8 mu m, respectively. The laser beam is irradiated: perpendicular to the substrate such that the induced absorption along the extended portion of the laser beam focal line is perpendicular to the plane of the substrate; and at an angle of greater than 0[deg] relative to the plane of the substrate such that the induced absorption is carried out at = 30[deg] . The method further comprises applying mechanical forces and/or thermal stresses to the substrate using a carbon dioxide laser during and/or after the generation of induced absorption within the substrate, non-uniformly heating the substrate, and cooling the substrate and then separating into parts by the crack formation between the extended portions. An independent claim is included for a device for laser processing a flat substrate.