The wave propagation in the analysis of the discrete method such as finite element method is examined for one dimensional structure. The transfer matrix method is adopted and the phase velocity, group velocity and equivalent damping ratio are explicitly solved from the eigenvalue of transfer matrix. From this examination, it is clarified that the propagating waves show the dispersion even if the continuum body is analyzed. In order to improve the wave propagation property, the optimal consistent mass ratios are derived, which give the same phase velocity or group velocity as those of the rigorous solution.