The analytical solution for the scattering of electromagnetic plane waves from an infinitely long homogeneous cylinder of arbitrary material, in an eccentric coating at oblique incidence, is presented. The solution is determined by solving the scalar wave equation in the cylindrical coordinates, for the various geometric regions and by applying the boundary conditions at the material interfaces. Furthermore, the translational addition theorem of Bessel functions is utilized for transferring the fields component between two cylindrical coordinate systems. Both polarizations of the incident plane wave (TM and TE with respect to the z -axis) are considered. The resulting solution consists of a system of eight coupled equations for the unknown expansion or scattering coefficients. Expressions for the extinction, scattering, and back scattering cross sections are presented. A numerical algorithm for the solution is developed, implemented, and tested for several limiting and special cases. Comparisons of the results with those reported in the literature show excellent agreements. Numerical calculations indicate that the eccentric cylinder arrangement is easily distinguishable from that of the coaxial cylinders.