Acoustoelasticity is a nondestructive technique for determining applied and residual stresses in structural materials. It is based on the fact that the velocity of an ultrasonic wave varies as stress is applied to a material. In laboratory conditions, it has been demonstrated that acoustoelasticity can be used successfully [1–3], however, there are some difficulties which have delayed its practical applications. One of these difficulties is the fact that the change in velocity due to texture is of the same order as that which is due to applied stress. This means that the convenient acoustoelastic relations for an isotropic material become more complicated when anisotropic material properties are used.