In the wafer producing apparatus of this invention, wafers each obtained by a slicing operation of a plurality of slicing devices are transported to a common finishing device by a transport device for chamfering. When the wafer is transferred to the transport device, an identification signal for identifying the slicing device by which the wafer is obtained is stored in an identification signal storage device. When the wafer is transferred from the transport device to the finishing device, the identification signal stored in the identification signal storage device is transmitted on a finish control device. Upon completion of the chamfering operation to the wafer by the finishing device, the finish control device controls the finishing device to allow the wafer to be stored in one of a plurality of wafer storage cassettes corresponding to the inputted identification signal. Thereby, even in a case where a working speed of the working device for slicing out a wafer from an ingot differs greatly from a working speed of the finishing device for chamfering the wafer, the wafer producing apparatus can be operated with a high proficiency and wafers processed by the common finishing device can be accurately stored in the proper wafer storage portion.