Heat treatment and production methods such as rolling, forging, deep drawing, etc, induce residual stresses as well as texture changes in the billets. T1zese processes cause the billets to become anisotropic. In "Acoustoelasticity", residual stresses can not be determined unless the texture is already mown apriori or determined simultaneously. In the present article, the equations of particle motion in an anisotropic elastic medium in the presence of residual stresses and texture is considered for two cases of rolling processes. Using elastic wave propagation in the medium, the relationships between the wave velocity and the residual strains as well as texture parameters in special planes are obtained for the general case and then simplified for rolled billets. The residual stress effects on the wave velocities are also discriminated from the effects of texture. The analytical results are discussed and compared with the experimental results for the case of one-dimensional stresses in billets, showing good agreement.