A cylindrical grinder comprising: a support unit including an upper support device and a lower support device, in which an ingot of silicon single crystal with a conical top portion and a cut tail portion (1b, 8) can be interposed in a direction of the axis line between the upper support device and the lower support device, can be clampingly held and can be rotated around the axis line; and a grinding unit which is adapted to relatively move during use of the cylindrical grinder along the direction of the axis line of the ingot to traverse grind an outer circumference of the ingot, wherein the upper support device is placed at an upper position and the lower support device is placed at a lower position, so that the support unit can clampingly hold the ingot in a state in which the direction of the axis line of the ingot is disposed along a vertical direction, characterized in that the lower support device includes a lower holder for holding the conical top portion of the ingot in the direction of the axis line, the lower holder is provided with a conical lower engaging hole with a diameter which is gradually decreased from one surface facing the ingot side to the other surface with a central axis of the lower holder as a center, the lower engaging hole is formed to penetrate the lower holder from the one surface to the other surface, the upper support device includes an upper holder for holding the cut tail portion (1b, 8) of the ingot in the direction of the axis line, the upper holder is provided with a conical upper engaging hole with a diameter which is gradually decreased from one surface facing the ingot side to the other surface with a central axis of the upper holder as a center, the upper engaging hole is formed to penetrate the upper holder from the one surface to the other surface, the upper holder has a lower circular flat surface for supporting the cut tail portion (1b, 8) of the ingot of which a tail portion is cut, an ingot sensing rod which is mounted on the upper holder and is inserted into the upper engaging hole so as to be able to abut on the cut tail portion (1b, 8) of the ingot and to be able to sense the ingot when the upper holder is moved downward during use of the cylindrical grinder and the cut tail portion (1b, 8) of the ingot is clampingly held by the upper holder, and the cylindrical grinder further comprises a positioning means for positioning the ingot at a predetermined position by pressing the ingot, which is interposed between the upper support device and the lower support device in a horizontal direction during use of the cylindrical grinder. a support unit including an upper support device and a lower support device, in which an ingot of silicon single crystal with a conical top portion and a cut tail portion (1b, 8) can be interposed in a direction of the axis line between the upper support device and the lower support device, can be clampingly held and can be rotated around the axis line; and a grinding unit which is adapted to relatively move during use of the cylindrical grinder along the direction of the axis line of the ingot to traverse grind an outer circumference of the ingot, wherein the upper support device is placed at an upper position and the lower support device is placed at a lower position, so that the support unit can clampingly hold the ingot in a state in which the direction of the axis line of the ingot is disposed along a vertical direction, characterized in that the lower support device includes a lower holder for holding the conical top portion of the ingot in the direction of the axis line, the lower holder is provided with a conical lower engaging hole with a diameter which is gradually decreased from one surface facing the ingot side to the other surface with a central axis of the lower holder as a center, the lower engaging hole is formed to penetrate the lower holder from the one surface to the other surface, the upper support device includes an upper holder for holding the cut tail portion (1b, 8) of the ingot in the direction of the axis line, the upper holder is provided with a conical upper engaging hole with a diameter which is gradually decreased from one surface facing the ingot side to the other surface with a central axis of the upper holder as a center, the upper engaging hole is formed to penetrate the upper holder from the one surface to the other surface, the upper holder has a lower circular flat surface for supporting the cut tail portion (1b, 8) of the ingot of which a tail portion is cut, an ingot sensing rod which is mounted on the upper holder and is inserted into the upper engaging hole so as to be able to abut on the cut tail portion (1b, 8) of the ingot and to be able to sense the ingot when the upper holder is moved downward during use of the cylindrical grinder and the cut tail portion (1b, 8) of the ingot is clampingly held by the upper holder, and the cylindrical grinder further comprises a positioning means for positioning the ingot at a predetermined position by pressing the ingot, which is interposed between the upper support device and the lower support device in a horizontal direction during use of the cylindrical grinder.