A perturbation expansion technique for approximating the three dimensi
onal anisotropic elastic Green's function is presented. The method emp
loys the usual series for the matrix (I-A)(-1) to obtain an expansion
in which the zeroth order term is an isotropic fundamental solution. T
he higher order contributions are expressed as contour integrals of ma
trix products, and can be directly evaluated with a symbolic manipulat
ion program. A convergence condition is established for cubic crystals
, and it is shown that convergence is enhanced by employing Voigt aver
aged isotropic constants to define the expansion point. Example calcul
ations demonstrate that, for moderately anisotropic materials, employi
ng the first few terms in the series provides an accurate solution and
a fast computational algorithm. However, for strongly anisotropic sol
ids, this approach will most likely not be competitive with the Wilson
-Cruse interpolation algorithm.