Ultrasonic measurements have been used for a long time to quantitatively determine the elastic properties of solids from wavespeed measurements. The determination is based on measuring the speeds of propagation of various wave modes, propagating in specific directions of the solid. Various methods have been developed for these measurements including both continuous wave and pulsed or burst techniques. A traditional distinction can be done in the way the transducer(s) interact with the solid to be characterized. Contact techniques [1,2] have been supplemented by immersion systems [3,4] which often yield more reproducible results and which permit measurements to be easily made along different directions in the test specimen. For instance, an advanced immersion system using the principle of digital interferometry with the help of a cross-correlation technique and normal mode tracking algorithms was recently designed [51. By using the mode conversion process at a liquid-solid interface, quasi-longitudinal and quasi-transverse bulk modes can be generated in numerous directions in the interior of the solid. The design and implementation of specialized optimization algorithms [6] permit a precise determination of the elastic constants for various synthetic and natural composite materials [7,8]. Nevertheless, a principal limitation of the existing optimization procedures for recovering a material’s elastic constants has been the requirement of wavespeed data measured in principal planes, where some analytical expressions, providing the slowness curves, generally exist [9].