In the manufacture of hollow jet engine turbine blades, monitoring the wall thickness is an important component of quality control. Because of the inaccessibility of the inner air channel to mechanical probing, ultrasonics provides one of the few means by which the necessary measurements can be done. The complex shape of the blades and the fact that they are often acoustically anisotropic make this a challenging problem. Alternative techniques have been investigated[1] for the wall thickness measurements but ultrasonics still presents the best option, and hence the continued interest in this problem[2].