The　flow-induced　vibration　of　a　cylindrical　structure　is　a　very　common　problem　in　marine　environments　such　as　undersea　pipelines,　offshore　risers,　and　cables.　In　this　study,　the　vortex-induced　vibration　(VIV)　of　an　elastically　mounted　cylinder　at　a　low　Reynolds　number　is　simulated　by　a　transient　coupled　fluid-structure　interaction　numerical　model.　Considering　VIV　with　low　damping　ratio,　the　response,　hydrodynamic　forces,　and　vortex　shedding　modes　of　the　cylinder　is　systematically　analyzed　and　summed　up　the　universal　rule　under　different　frequency　ratios.　On　the　basis　of　the　analysis,　we　find　that　the　frequency　ratio　a　is　a　very　important　parameter.　It　decides　the　locked-in,　beat,　and　phase-switch　phenomena　of　the　cylinder,　meanwhile,　it　also　influence　the　vortex　mode　of　the　cylinder.　The　trajectory　of　the　two　degrees　of　freedom　(2　DOF)　case　at　different　natural　frequency　ratios　is　discussed,　with　most　trajectories　having　a　＂figure　of　8＇＇　shape　and　a　few　having　a　＂crescent＇＇　shape.　A　fast　Fourier　transformation　technique　is　used　to　obtain　the　frequency　characteristics　of　the　vibration　of　the　cylindrical　structure.　Using　the　2　DOF　cylinder　model　in　place　of　the　1　DOF　model　presents　several　advantages　in　simulating　the　nonlinear　characteristics　of　cylindrical　structures,　including　the　capacity　to　model　the　crosswise　vibration　generated　by　in-line　vibration.