An ultrasonic wave propagating through a microscopically inhomogeneous medium, such as polycrystalline materials, is subject to scattering at the grain boundaries. The fraction of energy removed from the incident wave is responsible for important phenomenon like attenuation, dispersion, and background “noise” associated with a given ultrasonic inspection system. Since the backscattered signals tend to mask the signals from small and subtle defects, the estimation of probability of detection of such defects requires the quantitative description of these signals. Although considerable attention has been given to the understanding of mean propagation characteristics of an ultrasonic beam, until recently there have been relatively little efforts devoted towards rigorous treatments of backscattered signals. In this research, we attempt to include some degree of multiple scattering in the calculation of the backscattered signals by developing a formalism that relates mean wave propagation characteristics to the noise. © 2003 American Institute of Physics