Ultrasonic waves have been used in recent years to detect defects and damages in fiber-reinforced composite materials (see [1] for relevant references). A priori knowledge of how sound wave propagates through the composite medium is essential for using ultrasonic techniques in nondestructive evaluation. In the past, the problern of scattering by inclusions, such as fibers, has been studied extensively [2]–[3]. Most of the studies in the literature assume that the inclusions are perfectly boned to the matrix. However, defects are likely to exist along the fiber—matrix interfaces. As more interfacial defects are initiated, damages are developed within a layer of materials near the interface which will eventually lead to complete fiber debonding. Since interfacial damages may adversely affect the overall strength of the composites, it is important to be able to characterize and monitor the damage accumulation during manufacturing processes and engineering applications of the composites. Thus, developing theories and techniques to characterize interfacial strength, toughness and the amount of damages is warranted. To serve this purpose, the effects of interfacial damages on the behavior of wave propagation in fiber-reinforced composites need to be studied.