A simple procedure to analyze multilayered transmission lines with circular or quasi-circular uniaxial anisotropic dielectric layers is presented. It is based on an extension of the discrete mode matching method to analyze conformal structures with anisotropy. A generalized relation of the field components, which can be represented by a full-wave hybrid matrix for each layer, is used and then the dyadic Green’s function is obtained using a full-wave equivalent circuit of the structure. The application is demonstrated by computing dispersion characteristics for graded-index optical fibers, elliptical waveguides, and elliptical stripline structures with uniaxial anisotropic dielectric.