Inthiswork,dynamiccompositeanalysistruncatedsandwichconicalshells(STCS)withdifferentboundaryconditionsunderlowvelocityimpactwasinvestigatedanalytically,accordinghigherordersandwichpaneltheory.ImpactoccurredatthetopfacesheetandthecontactforcehistoryispredictedusingtwosolutionmodelscalculatedapplyingprincipalofHamiltonbyconsideringthedisplacementcontinuityconditionsbetweenthelayers.Forobtainingthedisplacementandcontactforcehistories,thedifferentialquadraturemethod(DQM)isutilised.Inthisinvestigation,theeffectsoflayerlaminanumber,conesemivertexangle,boundaryconditionsandimpactvelocityontheimpactresponsearestudied.