In a framework where a flaw is regarded as the spatial variation of the density and the elastic constants of the host medium, we derive a matrix scattering formalism. We introduce a bivariational principle for the scattering amplitude and use it to develop an optimal‐type approximation scheme. We consider the implications of reflection‐plane symmetry and show that when the incident and scattered waves lie in this plane, certain polarized, scattering amplitudes are zero. We develop a ’’partial‐wave’’ expansion for any flaw of spherical symmetry and reduce this scattering problem to a feasible numerical computation.