Revealing　the　propagation　properties　of　ultrasonic　guided　wave(UGW)in　a　waveguide　is　foundational　basis　for　applying　UGW　technique　for　structural　health　monitoring.　The　goal　of　this　paper　is　to　investigate　the　propagation　characteristics　of　elastic　waves　in　an　elliptical-rod.　In　elliptical　coordinates,　directional　semi-analytical　finite　element　method　is　introduced　to　establish　the　governing　equation　based　on　variational　principle.　The　phase　velocity　dispersion　curves　calculated　by　the　proposed　method　are　perfectly　matched　with　the　analytical　solution　results,　which　validates　the　feasibility　of　the　proposed　method.　Furthermore,　the　variation　of　dispersive　curves　vs.　long-to-short　axis　ratio　or　material　properties　is　investigated.　The　obtained　results　testify　that　the　directional　semi-analytical　finite　element　method　can　be　applied　for　calculating　the　dispersive　curves　of　an　elliptical-rod,　which　provides　a　theoretical　basis　for　UGW　techniques　for　elliptical-rod　inspection.　©,　2015,　The　Editorial　Board　of　Journal　of　Basic　Science　and　Engineering.　All　right　reserved.