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.　©　2018,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.