The　interaction　between　soil　layer　and　a　pile　with　elastic　bottom　boundaries　was　investigated　theoretically.　The　pile　was　assumed　to　be　vertical　and　elastic,　and　the　soil　was　considered　as　linear　visco-elastic　layer　with　hysteretic　damping.　The　soil　layer　was　studied　at　first　and　the　vibration　displacement　solution　with　undecided　constants　of　soil　layer　was　used　in　the　analysis　of　pile　response.　The　pile　response　to　a　harmonic　torque　was　obtained　in　a　closed　form　and　used　to　define　complex　stiffness　at　the　level　of　the　pile　top.　The　dimensionless　parameters　of　the　problem　were　identified.　Based　on　the　solution,　a　parametric　study　was　conducted　to　determine　the　main　features　of　dynamic　reactions　of　soil　layer　and　the　soil-pile　interaction　in　vertical　vibrations.