Abstract: In this paper, dispersion relations for three-dimensional waveguides with linear boundary cross-section were proposed by using analytic and directional semi-analytical method. The results show that the directional semi-analytical method combined analytical approach can be used to compute the dispersion curves for the longitudinal mode. The propagation characteristics of the longitudinal mode are affected by the straight boundary of the cross-section. When the symmetry of the cross section decreases, the group velocity of the mode appears to decrease sharply. At the end, an experimental device was set up, and the proposed method was proved by the experiment.