The　rational　approximation　is　an　important　tool　for　establishing　a　dynamic　analysis　model　in　time　domain　for　semi-infinite　water　and　soil.　It　accurately　represents　the　interaction　between　the　semi-infinite　medium　and　an　engineering　structure.　Current　research　on　rational　approximation　method　focuses　mainly　on　the　establishment　of　time-domain　analysis　models.　However,　the　stability,　accuracy,　and　calculation　efficiency　of　the　rational　approximation　model　cannot　be　guaranteed　simultaneously.　Based　on　linear　system　control　theory,　this　work　decomposes　the　continuous-time　rational　approximation　(CRA)　and　the　discrete-time　rational　approximation　(DRA)　into　a　combination　of　first-　and　second-order　subsystems,　and　the　stability　boundaries　for　the　identified　parameters　are　established　according　to　the　stability　conditions　of　each　subsystem.　A　genetic　algorithm　and　a　sequential　quadratic　programming　algorithm　are　used　to　construct　a　parameter　identification　method　that　can　ensure　stability　in　the　time　domain.　Through　parameter　identification　of　complex　frequency　response　functions,　it　is　demonstrated　that　the　method　proposed　in　this　work　can　guarantee　the　stability　and　accuracy　simultaneously,　and　the　calculation　efficiency　is　also　substantially　improved　over　that　of　the　existing　methods.