In cylindrically anisotropic, radially inhomogeneous materials, e.g. tree t
runks, the elastic constants referred to a cylindrical coordinate system de
pend on the radius but not the angle. The elasticity of these media is deve
loped in analogy to layered media in terms of eigenfunction expansions. Gre
en's functions for hollow and full cylinders under various boundary conditi
ons are constructed.