Abstract: A method for the separative processing of brittle-hard materials is provided. The method includes irradiating a surface of a workpiece made of brittle-hard material with a laser beam having a wavelength sufficient so that light of the laser beam is absorbed at the surface and so that the workpiece is heated to create a first temperature gradient in a direction from the surface to an interior of the workpiece; guiding the laser beam over the surface along an irradiated region; forming a second temperature gradient along the surface between the irradiated region and a non-irradiated region adjacent the irradiated region, the first and second temperature gradients interacting in such a way that, on account of thermomechanical stresses, the workpiece is separated below the surface with a portion of the workpiece being severed in the form of a chip.