Scattering of elastic waves by complex defects is investigated. In previous work the Distorted Wave Born Approximation was developed, in which a general shaped defect is represented as a sphere S and a remainder volume R, the latter being treated in first order perturbation theory. The DWBA was used to study scattering by a sequence of defects representing increasingly larger deviations from spherical; comparisons with experiment and other theories were made. This approach breaks down when scattering by R is of similar magnitude as by S. Such is the case for complex defects such as two spheres, or a sphere and a crack emanating from it. To treat such situations, a multiple scattering formalism was developed.