The ultrasonic examination of cast stainless steel components found in nuclear reactors has been plagued by problems such as difficulties in achieving sufficient penetration, poor signal-to-noise ratios, false indications, and mislocated flaws. One factor which plays an important role in these problems is anisotropy of the material, whereas many metal components can be viewed as isotropic, having randomly oriented, equi-axed grains, such is not the case for cast austenitic steels, in which the structure tends to crystallize with the [100]-axis of each grain parallel to the local thermal gradient. A consequence is that the ultrasonic wave speeds vary with direction, which in turn leads to such phenomena as beam skewing and excess beam divergence. The materials, anisotropic or not, can also exhibit large grain sizes which can lead to excess attenuation and background noise. Much effort has been placed on classifying the various microstructures and determining their elastic properties as well as studying beam propagation through them [1–8]. The theoretical modeling of beam propagation in anisotropic and inhomogeneous materials has also received much attention recently [9–16].