A wafer is produced from a compound single crystal ingot having end surface. A separation plane is formed by setting the focal point of a laser beam inside the ingot at a predetermined depth from the end surface. The depth corresponds to the thickness of the wafer to be produced. The laser beam is applied to the end surface to form a modified layer parallel to the end surface and cracks extending from the modified layer, thus forming the separation plane. The ingot has first atoms having a larger atomic weight and second atoms having a smaller atomic weight, and the end surface of the ingot is set as a polar plane where the second atoms are arranged in forming the separation plane. After producing the wafer from the ingot, the first end surface is ground to be flattened.