The presence of a state of residual stress in a material can impair its structural quality by adversely affecting its elastic limit, yield point, etc.1 Most common nondestructive measurements of residual stress use x-ray techniques.2 However, these techniques determine only the surface residual stresses, while in many practical cases knowledge of the bulk residual stresses is desired. Ultrasonic methods3,4 appear most natural for measuring bulk residual stress but are used infrequently, in part because of difficulty in adequately measuring small effects and in part because of the absence of theoretical results treating the inhomogeneous nature of residual stress fields.