Method and device for cutting flat work pieces of a brittle material

The invention is based on a method for cutting flat work pieces made of a brittle material, in particular glass or ceramic, in which a laser beam having a linear beam profile followed by a cold spot is moved along a dividing line having a specified contour. A preferred application of the method is in the cutting of flat glasses. The method of making a freeform cut on a work piece made of brittle material, such as glass, includes producing a linear focal point from a laser beam and a cold spot following the linear focal point on the work piece so that at least 60 percent of a laser beam energy output is concentrated at opposite ends of the linear focal point; moving the linear focal point along a specified contour for forming the cut and adjusting a length of the focal point according to a contour line curvature, so that the opposite ends lie on the contour, even when the contour is curved, in order to make the freeform cut. The device for performing this method includes a numerical trajectory control device () for positioning the linear focal point as it moves along the contour and a profile control device () cooperating with the numerical trajectory control device () for controlling a length (S) of the linear focal point ().