By developing the second-order interpolation function from the linear one

the second-order finite element is constructed to analyse the eigenvalue problem of a waveguide partially filled with anisotropic dielectric material. Dispersion curves of rectangular waveguides loaded with rectangular anisotropic dielectric rods are calculated and compared with the results obtained by other methods. Field distribution of a dielectric loaded waveguide is also calculated by using two types of elements. Two approximate formulas for calculating HE and EH modes are presented. The finite element analysis based on these two formulas is described and the numerical results are discussed.