  We provide an analytical solution for the elastic fields in a two-dimensional
unbounded isotropic body with a rigid inclusion. Our analysis is based on the
boundary integral formulation of the elastostatic problem and geometric
function theory. Specifically, we use the coordinate system provided by the
exterior conformal mapping of the inclusion to define a density basis functions
on the boundary of the inclusion, and we use the Faber polynomials associated
with the inclusion for a basis inside the inclusion. The latter, which
constitutes the main novelty of our approach, allows us to obtain an explicit
series solution for the plane elastostatic problem for an inclusion of
arbitrary shape in terms of the given arbitrary far-field loading.
