Composite structures, which are widely used in many critical applications in industry, consist of different elastic materials formed in layers. The layers are bonded together along common faces, but it can often happen that the bonding is imperfect, and cracks or weak bonding occur at the interface. The presence of critical defects can cause premature failure. It is of importance to detect interface cracks and weak interlayers nondestructively, and one of the most practical methods for the detection utilizes the scattering of elastic waves, which may convey quantitative information on the defects.