The far field characteristics are examined for a circular cylinder with two axial slots covered by an eccentric dielectric material. Solutions are found by applying the boundary-value method to the wave functions of the fields. The addition theorem and the orthogonality of Bessel and trigonometric functions are respectively used to find an infinite series expressions. Numerical results are obtained by shortening the produced series to a finite number of terms due to the convergence of the summation and compared to previous works.