The　localization　of　time　convolution　relation　of　generalized　force　and　displacement　has　been　the　key　to　the　construction　of　an　pricise　and　infinite-domain　FEM　model　used　for　the　time-domain　soil-structure-interaction　analysis.　The　physical　model　method　is　used　in　this　paper　to　localize　time　convolution　as　it　is　compatible　to　FEM.　A　novel　model　of　high-order　spring-dashpot-mass　(HSDMM)　is　constructed　using　the　time-and　frequency-domain　equations　as　well　as　the　corresponding　normal　equations.　The　transformation　relation　for　the　parameters　used　in　these　two　types　of　equations　is　also　otained.　The　sufficient　and　necessary　dynamic　stability　conditions　for　the　proposed　model　are　proposed,　and　a　parameter　identification　method　(PIM)　considering　stability　condition　is　developed　based　on　the　penalty　function　and　the　genetic-simplex　algorithm.　The　systemic　and　concise　HSDMM　with　the　proposed　PIM　can　be　readily　incorporated　into　a　dynamic　commercial　software　and　the　established　dynamically　stable　soil-structure　interaction　problem　can　be　solved　even　using　an　explicit　time　stepping　integration.　Finally,　the　performance　of　HSDMM　with　the　proposed　PIM　is　evaluated　by　analyzing　a　semi-infinite　rod　on　elastic　foundation　with　it　and　comparing　the　results　to　the　results　obtained　with　several　existing　models.