Exact　representation　of　unbounded　soil　contains　the　single　output-single　input　relationship　between　force　and　displacement　in　the　physical　or　transformed　space.　This　relationship　is　a　global　Convolution　integral　in　the　time　domain.　Rational　approximation　to　its　frequency　response　function　(frequency-domain　convolution　kernel)　in　the　frequency　domain,　which　is　then　realized　into　the　time　domain　as　a　lumped-parameter　model　or　recursive　formula,　is　an　effective　method　to　obtain　the　temporally　local　representation　Of　unbounded　soil.　Stability　and　identification　for　the　rational　approximation　are　studied　in　this　paper.　A　necessary　and　sufficient　stability　condition　is　presented　based　oil　the　stability　theory　of　linear　system.　A　parameter　identification　method　is　further　developed　by　directly　solving　a　nonlinear　least-squares　fitting　problem　using　the　hybrid　genetic-simplex　optimization　algorithm,　in　which　the　proposed　stability　condition　as　constraint　is　enforced　by　the　penalty　function　method.　The　stability　is　thus　guaranteed　a　priori.　The　infrequent　and　undesirable　resonance　phenomenon　in　stable　system　is　also　discussed.　The　proposed　stability　condition　and　identification　method　are　verified　by　several　dynamic　soil-structure-interaction　examples.　Copyright　(C)　2009　John　Wiley　&　Sons,　Ltd.