The invention concerns a method for separating plate-shaped workpieces of mechanically brittle and nonmetal materials along any contour desired, comprising the following steps: Scratching of separating lines along the contour up to a depth T by means of a cutting device in at least one side of the plate-shaped workpiece is hereby characterized in that the plate-shaped workpiece is stimulated to bending vibrations at a vibration amplitude along the separating lines, so that the plate-shaped workpiece is completely separated along the separating line.