A matrix theory is developed for investigating the scattering of elastic waves in solids by an obstacle of arbitrary shape. The scattering matrix which depends only on the shape and nature of the obstacle relates the scattered field to any type of harmonic incident field. Expressions are obtained for the elements of the scattering matrix in the form of surface integrals around the boundary of the obstacle, which can be evaluated numerically. Using the principle of reciprocity and the conservation of energy, the scattering matrix is shown to be symmetric and unitary. These properties are essential to assure the accuracy of numerical calculations. Both two‐ and three‐dimensional problems are discussed, and the obstacle may be an elastic inclusion, a fluid inclusion, a cavity, or a rigid inclusion of arbitrary shape.Subject Classification: [43]20.15, [43]20.30.