Determining the elastic moduli of anisotropic materials via non-destructive testing techniques is one of the most difficult subjects of acoustoelasticity theory today. The major difficulty comes from the fact that the elastic waves propagating in anisotropic media have different phase and group velocities in both magnitude and direction, which was considered to greatly complicate the analysis of the problem. Therefore, previous work in this area has been restricted to either measurements conducted only in symmetry planes, as mentioned in [1,2], or the slight anisotropy case in which the ultrasonic measurement was approximately related to the phase velocity, such as [3,4].