Abstract: A method of cutting a brittle workpiece comprises applying to the surface of the workpiece a pointed tool, applying high frequency vibrations in a longitudinal direction to the tool, and moving the tool along a line to be cut of the workpiece while applying substantially steady longitudinally directed pressure to the tool. Stress is thereby applied to the workpiece as a combination of short impulses and steady direct stress and the breaking stress of the material would be attained coincident with the peak oscillatory stress. Crack propagation would therefore proceed by a series of stepwise fractures induced by successive cyclic stress peaks, resulting ultimately in the separation of the workpiece into two pieces.