ThispaperpresentstheHillinstabilityanalysisofTensionLegPlatform(TLP)tetherindeepsea.The2-Dnonlinearbeammodel,whichisundergoingcoupledaxialandtransversevibrations,isapplied.ThegoverningequationsarereducedtononlinearHillequationbyuseoftheGalerkin'smethodandthemodessuperpositionprinciple.TheHillinstabilitycharteduptolargeparametersisobtained.AnimportantparameterMisdefinedandcanbeexpressedasthefunctionsoftetherlength,theplatformsurgeandheavemotionamplitudes.Someexamplestudiesareperformedforvariousenvironmentalconditions.Theresultsdemonstratethatthenonlinearcouplingbetweentheaxialandtransversevibrationshasasignificanteffectontheresponseofstructure.ItneedstobeconsideredfortheaccuratedynamicanalysisoflongTLPtethersubjectedtothecombinedplatformsurgeandheavemotions.
