Dynamic　responses　of　soil　foundation　are　difficult　to　analyze,　though　it　is　related　to　kinds　of　practices.　In　this　paper,　dynamic　responses　of　soil　foundation　under　dynamic　load　were　analyzed　theoretically.　Perturbation　method　was　used　to　obtain　the　theoretical　solution.　Controlling　equations　were　about　liquid-solid　two-phase　media.　Flow,　function,　and　potential　function　were　introduced　to　decouple　the　controlling　equations.　Then,　perturbation　expansion　was　introduced　into　the　equations　of　flow,　function,　and　potential　function.　The　responses＇　characteristics　are　discussed.　©　2013　American　Society　of　Civil　Engineers.