Abstract: A method of cutting non-metallic materials, specifically glass, resides in the heating of the material by an incident beam of radiation being effected to a temperature short of its softening point, with the rate of relative displacement of the beam and of the material, and the region of the heated zone which is locally cooled being selected to form a blind crack in the material. The method provides for increasing substantially the cutting speed and accuracy, and also for controlling the depth, shape and angle of the cut face formed by the crack.