Efficient　and　reliable　dynamic　modelling　and　analysis　is　critical　to　the　shape　control　and　estimate　of　a　backbone　continuum　manipulator.　This　paper　presents　a　novel　dynamic　modelling　method　to　investigate　the　deformation　modal　properties　of　a　vertical　stretch-retractable　continuum　manipulator　(VSRCM)　under　the　tip　horizontal　load.　Based　on　the　equivalence　of　the　elastic　bending　potential　energy,　this　method　simplifies　the　backbone　continuum　manipulator　to　a　single　beam,　an　equivalent-guided　beam　(EGB).　One　end　of　the　EGB　is　fixed,　and　the　other　end　is　guided.　The　modal　dynamics　model　of　the　EGB　is　then　established　by　employing　the　vibration　theory　of　a　continuous　beam,　and　the　modal　properties　of　the　continuum　manipulator　are　analyzed.　Static　and　Dynamic　experiments　of　the　VSRCM　are　performed　to　validate　the　dynamic　modeling　method　through　the　comparison　and　analysis　of　the　free　dynamic　response　and　frequency　properties　of　the　continuum　manipulator.　To　analyze　the　free　dynamic　response,　the　large　deflection　static　model　with　tip　horizontal　load　is　also　established　based　on　the　elliptic　integral　approach.　Experimental　results　and　comparison　demonstrate　that　the　static　model　is　efficient　and　precise　to　predict　the　large　deformation,　and　the　modal　dynamic　models　well　reflect　the　actual　vibration　modal　characteristics　of　the　VSRCM.　©　2019　IEEE.