A method of producing a wafer includes forming a peel-off layer in a hexagonal single-crystal ingot by applying a laser beam having a wavelength transmittable through the ingot while positioning a focal point of the laser beam in the ingot at a depth corresponding to the thickness of a wafer to be produced from an end face of the ingot, generating ultrasonic waves from an ultrasonic wave generating unit positioned in facing relation to the wafer to be produced across a water layer interposed therebetween, thereby to break the peel-off layer, and detecting when the wafer to be produced is peeled off the ingot based on a change that is detected in the height of an upper surface of the wafer to be produced by a height detecting unit positioned above the upper surface of the wafer to be produced across the water wafer interposed therebetween.