In　this　paper,　a　numerical　model　based　on　the　finite　difference　method,　the　implicit　Euler　method　and　the　Newton-Raphson　method　are　proposed　to　study　the　axial-coupling　vibration　response　of　the　elastic　and　viscoelastic　pipes　caused　by　water　hammer.　In　the　considered　system　of　reservoir-pipeline-valve,　the　mathematical　model　of　axial　vibration　in　fluid-conveying　straight　pipes　concerning　the　viscoelasticity　effect　of　pipe-wall　is　the　hyperbolic　four-equation　model.　Meanwhile,　considering　the　Poisson　coupling　and　the　junction　coupling　in　the　pipeline,　the　numerical　results　are　in　good　agreement　with　other　numerical　and　experimental　solutions.　It　indicated　that　both　of　two　coupling　effects　on　the　axial　vibration　of　the　pipeline　cannot　be　ignored.　When　only　Poisson　coupling　is　considered,　the　fluctuation　of　pressure　head　increases　obviously　and　the　vibration　is　accelerated.　On　the　other　hand,　while　the　Poisson　coupling　and　the　junction　coupling　are　considered　simultaneously,　vibration　become　more　complex　and　the　response　curve　of　pressure　head　is　more　irregular.　Moreover,　the　distinct　differences　in　response　characteristics　of　axial　vibration　were　found　between　the　viscoelastic　pipe　and　the　elastic　pipe.　The　pulsating　pressure　head　of　viscoelastic　pipe　will　decreases　rapidly　with　time,　and　the　phase　is　delayed　with　respect　to　elastic　pipe,　while　the　pressure　head　of　the　elastic　pipe　has　no　attenuation　tendency.　©　2017,　Nanjing　Univ.　of　Aeronautics　an　Astronautics.　All　right　reserved.