A SiC wafer is produced from a single crystal SiC ingot. Wafer producing apparatus includes a holding unit for holding the ingot, a flattening unit for grinding the upper surface of the ingot, thereby flattening the upper surface, a laser applying unit for setting the focal point of a laser beam having a transmission wavelength to the ingot inside the ingot at a predetermined depth from the upper surface of the ingot, the predetermined depth corresponding to the thickness of the wafer to be produced, and next applying the laser beam to the ingot to thereby form a separation layer for separating the wafer from the ingot, a wafer separating unit for holding the upper surface of the ingot to separate the wafer from the ingot along the separation layer, and a wafer storing unit for storing the wafer separated from the ingot.