Most structural materials are polycrystalline, that is, they are composed of numerous discrete grains, each having a regular, crystalline atomic structure. The elastic properties of the grains are anisotropic and their crystallographic axes are differently oriented. When an ultrasonic wave propagates through such a polycrystalline aggregate, it is scattered at the grain boundaries. The fraction of sound energy thus removed from the main beam is responsible for important phenomenons like attenuation and dispersion of the main beam, and background “noise” associated with a given ultrasonic inspection system. The amount of sound energy removed from the main beam depends on the size, shape, and orientation distributions of the grains. If the grains are equiaxed and randomly oriented, propagation direction of the ultrasonic wave has no effect upon the magnitude of the scattered energy. Such is not the case when an acoustic wave travels through materials like centrifugally cast stainless steel and austenitic stainless steel welds, which are used extensively in nuclear power plants. The microstructures of these stainless steels vary from randomly oriented, equiaxed grains to highly oriented, columnar grains.1,2 Since the backscattered signals tend to mask the signals from small and subtle defects, the estimation of probability of detection of such defects requires quantitative description of these signals. Consequently, an effort has been undertaken in this research to quantify the backscattered signals from microstructures with favored grain orientation and grain elongation.