To provide a laser beam machining apparatus and a laser beam machining method where a crack line having a desired aspect ratio is formed on a transparent dielectric material substrate such as a sapphire, and, the material substrate is diced with the crack line as a starting point, thus two slant faces with prescribed angles are formed at the cut edges, so as to be a state where the corners are chambered, and the material substrate is cut.

A laser light source 101 generates laser light for machining in a wavelength which is not absorbed in a workpiece 10. An optical system 105 for generating astigmatism forms a tetrahedron type condensing spot 9 from the laser light for machining passed through a telescope optical system 103. An objective lens 109 condenses the laser light for machining reflected by a dichroic mirror 107, and emits the same to the workpiece 10 placed on a stage 113. The stage 113 is subjected to driving (parallel translation and rotation) so as to form a crack line to the workpiece 10 on the stage 113 along a machining predetermined line and a machining predetermined position.