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We present a multiple scattering formalism that was developed in order to calculate elastic wave scattering by complex defects. The formalism is based on an expansion of the T matrix in terms of single scatterer T matrices; we include all single and double scattering processes. The method has been numerically implemented for the case of two spherical cavities; the interaction terms were found to be small, which indicates that other problems of interest, such as a subsurface spherical cavity or crack can also be treated.