Abstract: The explicit expressions for the stiffness and mass matrices of the tapered beam conforming elements with displacement functions based on the 3rd, 5th and 7th order polynomial respectively are given, and a general method for evaluating the stiffness and mass matrices of even higher order beam element with arbitrary odd power is also developed. Then by means of these elements are calculated the first five natural frequencies and corresponding modes of these elements are calculated the first five natural frequencies and corresponding modes of the linearly tapered beams with rectangular cross section in six manners under various boundary conditions （e. g. fixed-fixed, simply supported-simply supported, cantilever, etc. ） Numerical results are presented for several typical cases. The results indicate that the higher order element exhibits better convergence than the lower order element in all cases without imposition of natural boundary conditions. Otherwise the higher order element would lead to worse results than the lower order element for deeply tapered beams with a few elements used in calculation Hence, it may be concluded that the reason for the worse convergence of the higher order element in some cases is the imposition of the natural boundary conditions in advance, but it is not necessary for the displacement variational principle.