Abstract: A laser machining apparatus capable of performing high-quality and precise cuts on sharply angled or complexly configured portions of a plate-type workpiece with minimum burn-through loss of material due to thermal saturation. In accordance with the invention, values are prestored representing optimum laser output with respect to the speed of the laser beam relative to the workpiece for various types of workpiece material and thickness of the workpiece. These values are read out and the laser beam controlled in accordance therewith during cutting operations. Some of the values represent a continuous output and are applied for higher speed cutting, while others represent a pulsed output and are applied for lower speed cutting.