Two　new　types　of　high-order　lumped-parameter　models　(LPMs)　for　foundation　vibrations　are　proposed.　The　parameters　of　LPMs　are　obtained　by　comparing　the　continued-fraction　dynamic-stiffness　equations　of　new　LPMs　with　the　continued-fraction　expansions　of　a　rational　function　in　complex　frequency　approximating　foundation　frequency　response.　Compared　with　the　existing　high-order　LPMs,　the　proposed　LPMs　are　easier　to　extend　to　high　orders,　and　their　physical　configurations　are　condensed　and　independent　of　the　problem　analyzed.　Moreover,　due　to　the　dynamic　equations　of　LPMs　with　second-order　derivative　terms　in　time,　the　resulting　structure-foundation-soil　system　can　be　solved　by　an　explicit　time-integration　method.　The　effectiveness　of　the　proposed　LPMs　is　verified　by　analyzing　the　benchmark　problem　of　semi-infinite　rod　on　an　elastic　foundation　and　comparing　with　the　results　of　Wu-Lee　LPMs.