This study investigates the stress distribution in a transversely isotropic medium containing a spheroidal
cavity where the medium is under uniaxial tension in z;:iirection in one case and pure shear in
the plane of isotropy in another case. The technical approach used in this study combines exact analytical
and numerical methods. The exact analytical method is based upon three potential funct.ions taken
in terms of the Legendre associated functions of the first and second kind. The numerical method is
based upon the finite difference approach. Numerical results concerning the two loading conditions with
fi ve anisotropic materials are presented.