Radially transverse isotropic inclusions in homogeneous isotropic conductive and elastic media are considered. The Mellin transform method is used for the solution of the volume integral equations of the problems. The method reveals the tensor structure of the solution with precision to three scalar functions of the radial coordinate. The system of ordinary differential equations for these functions arises in the process of realization of the method. For multilayered radially transverse isotropic inclusions with constant elastic and conductive coefficients inside the layers, explicit equations for the fields inside the layers are obtained. An efficient numerical algorithm of solution for solving inclusions with an arbitrary number of transverse isotropic layers is presented.