Critically refracted longitudinal waves (LCR) offer considerable advantage in achieving nondestructive measurement of stress in engineering components and structures. Of the various wave types, the LCR is most sensitive to stress and least sensitive to texture. Also called the surface skimming longitudinal wave (SSLW), the LCR wave skims along just underneath the surface of a material at bulk wave speeds. Further, there is experimental evidence of frequency dependence where the higher frequencies concentrate their energy more toward the surface than do the lower frequency waves. This effect, which has not been fully explained theoretically, enables stress gradient evaluation below the surface. Further, there is observed scatter in the travel times found at low stress levels. At higher levels of stress, the data often become very linear. The specific nature of the LCR wave, acoustoelasticity, LCR probes and beam patterns, and methods for its excitation, are described. Probe frequencies from 1.0 to 20 MHz have been used. System travel-time repeatability is 0.01% or better and stress resolution of ±21 MPa (3 ksi) is obtained in typical applications. Tests showing the frequency dependence and the scatter observed at low levels will be discussed. Several applications described using the LCR technique for stress measurements include pressure vessels, piping, welds, titanium turbine engine blades, aluminum plate and a turbine rotor. Future applications and research using the technique will be mentioned.