Abstract: 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.