The　first-modal　frequency　and　damping　of　a　building　are　identified　by　using　the　earthquake　records　on　the　building　and　on　related　free-field　in　Alaska,　USA.　The　non-parameter　model　and　ARX　parameter　model　of　the　structure　are　used　in　the　identification　system,　and　soil-structure　interaction　system　and　structure　-system　are　both　identified.　By　comparing　the　results　obtained　from　the　identification　system　with　the　results　obtained　from　the　both　model　is　identical　in　low-frequencies,　and　but　the　amplitude　of　transfer　function　obtained　from　SSI　system　is　smaller　than　from　structure　system　itself,　especially　in　high-frequencies.　All　these　computations　are　realized　on　the　Matlab　platform.