  In this paper, we present a fast multipole method (FMM) for the half-space
Green's function in a homogeneous elastic half-space subject to zero normal
stress, for which an explicit solution was given by Mindlin (1936). The image
structure of this Green's function is unbounded, so that standard outgoing
representations are not easily available. We introduce two such representations
here, one involving an expansion in plane waves and one involving a modified
multipole expansion. Both play a role in the FMM implementation.
