Abstract: The brittle material cleavage-cutting apparatus of the present invention comprises a placing stand for holding a brittle material and beam scanning device for deflecting a laser beam from a laser source so that a brittle material placed on the placing stand is scanned along a planned cleavage-cutting line. By the beam scanning device, the laser-beam irradiation position on the brittle material is repeatedly moved in short cycles along the planned cleavage-cutting line.