Elastic-wave interactions with imperfect interfaces between two solids have important applications for their nondestructive evaluation. To model such imperfect interfaces non-classical boundary conditions (B.C.) are generally used. For fractured interfaces one can use micro-mechanical analysis to define the B.C. directly, such as the quasi-static (spring) model for cracked interfaces [1, 2]. These studies and more recent theoretical and experimental work [3, 4, 5] suggest that fractured interfaces can be modeled by such spring B.C. For interfaces with porosities/inclusions one can use thin multi-phase interfacial layers to model such solid-solid interfaces, and use asymptotic expansions to substitute for the interphases by equivalent interface B.C. [6, 7, 8]. Here “thin” means that the interfacial layer thickness-to-wavelength ratio is small. An important aspect of wave interaction is the effect of interface imperfection orientation when the interface symmetry axes deviate from the incident-wave plane. Typical examples for (a) a fractured interface with preferred crack orientation and (b) an interphase with cylindrical-like pores or inclusions are shown in Fig. 1.