The continuum theory of elastic wave propagation in deformed, anisotropic solids is reviewed with emphasis on those features which might be used to distinguish between stress induced changes in ultrasonic velocity and changes due to material anisotropy, such as would be produced by preferred grain orientation in a polycrystalline metal As noted by previous authors, one such feature is the difference in velocity of two shear waves, whose directions of propagation and polarization have been interchanged. In particular, when these directions fall along the symmetry axes of a rolled plate (assuming orthorhombic symmetry) and these are also the directions of principal stress, then the theory predicts that ρ(V 12 2−V 21 2) = T1−T2 where ρ is the density, Vij is the velocity of a shear wave propagating along the i-axis and polarized along the j-axis, and Ti is a principal stress component. In addition to being independent of the degree of texture, this relationship has the advantage that no microstructurally dependent acoustoelastic coefficient is involved. The applicability of this prediction of continuum theory to heterogeneous engineering materials such as metal polycrystals is discussed using previously reported stress dependencies of ultrasonic velocities, and new experiments to answer some remaining questions are described. A possible configuration for using the effect to measure the value of a uniform stress in a plate of unknown texture is proposed.