Considering　soil-pile　interaction　and　vertical　wave　effect　of　soil　around　pile,　the　dynamic　vertical　response　of　a　pile　in　time　domain　is　investigated　theoretically.　The　pile　is　assumed　vertical　and　with　elastic　bottom　boundaries　and　the　soil　is　considered　as　viscoelastic　layer　with　hysteretic　type　damping.　The　soil　layer　alone　is　solved　first　and　its　vibration　displacement　solution　with　undecided　constants　is　used　in　the　analysis　of　pile　response.　Then　by　solving　dynamic　equilibrium　equation　of　pile,　the　pile　response　to　a　harmonic　load　is　obtained　in　a　closed　form　and　a　semi-analytical　solution　of　the　velocity　response　of　pile　subjected　to　a　semi-sine　wave　exciting　force　is　also　given.　In　comparison　with　other　theories,　the　correctness　and　applicability　of　the　theoretical　solutions　presented　herein　are　verified.　Based　on　the　solution,　A　parametric　study　is　conducted　to　determine　the　main　features　of　dynamic　response　of　pile　in　time　domain.　It　is　shown　that　the　theoretical　curves　are　in　good　agreement　with　those　obtained　from　on-site　test.