The invention relates to a method for severing brittle flat materials, for example made of glass, ceramic, silicon, gallium arsenide or sapphire. The method includes the step of heating the flat material along desired dividing lines below its melting temperature by means of a laser alone desired separating lines. Then the material is shocked by a coolant jet so that a thermally-induced mechanical stress difference brings about a material separation. Traces are formed in the flat material in advance along the separation lines, so that the flat material has a lower breaking stress along the traces than in the unworked flat material, and the separation with the laser takes place along these traces.