We consider the inverse scattering problem for the shape determination of a rigid scatterer or a cavity in a homogeneous and isotropic elastic medium. Both problems are formulated in R2 for time‐harmonic fields and longitudinal or transversal incident plane waves. Representation of the scattered field as a single‐ or a double‐layer potential, equivalently, leads to a system of two nonlinear integral equations for the density and the parametrization of the boundary. A detailed numerical implementation is presented for computing the corresponding solutions of both systems and numerical reconstructions are given to show the effectiveness of the method.

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