The analytical solution for the linear elastic problem of an internal ring-shaped crack in a transversely isotropic hollow cylinder imbedded in a transversely isotropic medium is considered. The hollow cylinder is assumed to be perfectly bonded to the surrounding medium. This structure is subjected to uniform crack surface tractions. Because of the geometry and the loading, the problem is axisymmetric. The z=0 plane on which the crack lies, is also taken to be a plane of symmetry. The composite media consisting of the hollow cylinder and the surrounding medium extends to infinity in z and r directions. The mixed boundary value problem is formulated in terms of the unknown derivative of the crack surface displacement by using Fourier and Hankel transforms. The resulting singular integral equation is solved numerically for sample cases and stress intensity factors at the circumferential crack front are presented.