The problem is formulated for the scattering of long wavelength plane elastic waves by a single homogeneous obstacle in an infinite elastic medium. The problem differs from earlier studies in that discrete differences in the physical properties are permitted to exist at the boundary. Earlier treatments of the scattering problem in which the Green's function for the scatterer is a simple operation on the incident field are inadequate to account for the refraction of the field at the boundary. For the case of scattering of long waves by a spherical obstacle the scattered fields are shown to involve the elastic constants in identically the same way as does the static field for the same geometry in the presence of a uniform static field. As a special case a new solution is given for the static problem of the inhomogeneous inclusion. A wave equation is derived for the “average” field due to multiple scattering by a statistical distribution of spheres. The macroscopic wave parameters for the long wavelength approximation are obtained as a weighted contribution of the properties of the two components.