To assure that a plate-shaped brittle material is exactly cut into two plate pieces, a jig having a thread-shaped projection secured thereto in conformity with a predetermined pattern positionally coincident with a cut groove formed in the plate-shaped brittle material, an elastic member located on the cut groove side of the plate-shaped brittle material, and a plate-shaped brittle material to be cut into two plate pieces are placed on a table of a press machine one above another, and subsequently, a predetermined intensity of pressing power is applied to the jig from above by operating a pressing machine. Alternatively, a jig having a thread-shaped projection secured thereto, an elastic member located on the opposite side relative to the cut groove side of the plate-shaped brittle material, and a plate-shaped brittle material to be cut into two plate pieces may be placed on the press table one above another. Otherwise, a pair of jigs each having a thread-shaped projection secured thereto, a pair of elastic members one of which is located on the cut groove side of a plate-shaped brittle material and other one of which is located on the opposite side relative to the cut groove side of the plate-shaped brittle material, and a plate-shaped brittle material to be cut into two plate pieces may be placed on the press table one above another.