This study provides an analytic method for the calculation of the cutoff frequencies and waveguide modes of a partially filled eccentric coaxial cable. The method is based on the expressions of the involved electromagnetic fields in bipolar coordinate systems and the validity range of the solution is discussed. It is shown how the waveguide geometry and dielectric parameters may be selected to engineer the lined waveguide's spectral response. Numerical results are included which show good agreement with the corresponding results from full-wave simulations by commercial software.