Statics　modelling　is　critical　to　posture　deformation　analysis　and　shape　control　under　external　loads,　especially　large　deflections.　This　paper　presents　a　novel　statics　modelling　method　to　discuss　the　shape　deformation　of　an　extensible　continuum　manipulator　(ECM)　under　an　external　tip　load.　According　to　the　equivalence　of　the　elastic　bending　potential　energy,　the　ECM　is　simplified　as　an　equivalent-fixed-guided　beam　(EFGB)　with　the　corresponding　equivalent　bending　stiffness.　Subsequently,　a　large　deflection　statics　model　of　the　EFGB　is　established　based　on　the　continuous　beam　theory,　and　a　solution　is　calculated　by　employing　the　elliptical　integral　algorithm.　Further,　based　on　the　large　deflection　statics　model,　several　shape　simulations　under　different　external　tip　loads　of　the　ECM　are　discussed,　especially　the　shape　deformation　of　the　vertical　posture.　In　addition,　the　statics　experiments　of　the　ECM　are　performed　to　validate　the　presented　statics　modelling　method　by　comparing　the　shape　deformation　under　different　directions　of　the　external　tip　load　between　the　theoretical　and　experimental　value.　The　experiments　and　the　contrast　demonstrate　that　the　results　match　with　the　theoretical　solution　well,　and　that　the　proposed　statics　modelling　method　is　efficient　and　precise　for　predicting　the　shape　deformation　of　the　ECM.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.