A new method is applied to obtain the Green's tensor for a point sourc
e in a general anisotropic elastic homogeneous unbounded medium in the
form of an integral over the surface of a unit sphere. This represent
ation can be used to obtain, in the time domain, simple expressions fo
r the displacement held generated by a localized source with an arbitr
ary time dependence. The static term of the Green's tensor is transfor
med into an easily calculable form. A high-frequency asymptotic expres
sion is derived for the Green's tensor.