In　this　study,　a　high-order　accuracy　numerical　model　of　the　meshless　method,　called　generalized　finite　difference　method　(GFDM),　was　generalized　to　analyze　the　transverse　vibration　problem　of　pipe　conveying　fluid.　Based　on　the　differential　equation　of　transverse　vibration,　the　GFDM　and　the　Houbolt　methods　were　adopted　to　discretize　the　partial　differential　items　in　space　and　time,　respectively.　The　consistent　with　good　results　of　natural　frequency　and　the　amplitude　time　range　was　compared　with　the　theoretical　solution　and　other　numerical　results　reported　in　literature.　Meanwhile,　the　numerical　model　proposed　in　this　paper　has　good　stability　and　robustness　in　solving　the　vibration　response　of　pipe　conveying　fluid　by　comparing　with　the　vibration　amplitude　at　the　midpoint　with　different　total　number　of　points　N,　time　step　Δt　and　sub-region　selection　points　ns,　respectively.　Furthermore,　detailed　analysis　of　the　vibration　response　characteristics　with　several　typical　boundary　conditions　indicates　that　the　vibration　amplitude　at　the　midpoint　of　the　pined-pined　pipe　is　much　large　than　that　of　two　other　boundary　conditions,　and　the　vibration　frequency　of　the　clamped-clamped　pipe　is　more　fast　than　that　of　others.　Besides,　the　position　of　the　maximum　amplitude　of　the　vibration　is　shifted　to　the　weak　constraint　when　the　end　of　restrictive　condition　is　asymmetric.　©　2019,　Editorial　Office　of　Journal　of　Vibration　and　Shock.　All　right　reserved.