To　study　axial　coupled　vibration　response　of　a　fluid-conveying　pipeline　excited　by　water　hammer,　the　split-coefficient　matrix　finite　difference　method　(SCM-FDM)　combined　with　the　implicit　Euler　method　(IEM)　was　proposed　to　do　numerical　simulation　for　the　pipeline　4-quation　dynamic　model　with　fluid-structure　interaction.　The　proposed　SCM-FDM　was　simple,　easy　and　stable　to　implement　since　the　appropriate　difference　formulas　were　selected　according　to　the　direction　of　wave　propagation.　Compared　with　the　method　of　characteristics　lines　(MOCL),　SCM-FDM　avoids　time-consuming　calculations　of　spatial　or　temporal　interpolations.　To　verify　the　applicability　and　accuracy　of　SCM-FDM,　its　computation　results　were　compared　with　other　authors＇　numerical　results　and　those　of　the　water　hammer　theory,　they　agreed　well　each　other.　Furthermore,　the　effects　of　fluid　velocity,　fluid　pressure,　axial　pipe　vibration　velocity　and　pipe-wall　stress　on　the　system＇s　vibration　response　features　were　analyzed　in　two　cases　including　only　considering　Poisson　coupling　and　considering　both　Poisson　coupling　and　connection　one.　The　results　indicated　that　the　effects　of　both　two　couplings　on　the　axial　vibration　features　of　the　fluid-conveying　pipeline　can＇t　be　ignored;　Poisson-coupling　mainly　affects　amplitudes　of　vibration　response,　while　the　connection　coupling　affects　both　amplitude　and　frequency　of　vibration　response.　©　2018,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.