Assuming　that　the　soil　is　uniform　linear　viscouselastic　layer　with　viscous　damping,　the　time　domain　torsional　response　of　dynamically　loaded　pile　in　the　soil　layer　is　theoretically　investigated.　And　the　corresponding　solution　of　the　displacement　and　velocity　response　function　at　the　pile　top　end　in　frequency　domain　is　obtained　in　a　closed　form.　Then,　by　means　of　invert　Fourier　transform,　a　quasi　analytical　solution　of　velocity　response　of　the　pile　in　time　domain　subjected　to　a　half　sine　wave　excitation　force　is　obtained.　Based　on　the　solution,　a　parametric　study　is　conducted　to　determine　the　main　features　of　the　soil-pile　interaction,　and　the　special　influences　of　viscous　damping　of　soil　layer　are　also　discussed.