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In-service breakage of railway wheels is a serious issue faced by the railways. Such accidents usually result in derailment with property damage, and sometimes, loss of life. Many railways and research institutions have developed non-destructive test methods to prevent these events and to retire the wheels before failure takes place. One of the most promising alternative methods for this type of inspection is the measurement of stress at the wheel rims by ultrasonic evaluation, with the use of electro-magnetic or piezoelectric probes. One of the difficulties found in the use of this method is the practical determination of the acoustoelastic constant. This paper shows how to establish this constant in a practical manner, as well as its use in establishing the stress in forged railway wheels using critically refracted longitudinal waves.