Taking axisymmetric wave effect of soil into account, longitudinal vibration of pile in viscous damping layered soils undergoing arbitrary load is theoretically investigated. An analytical solution for admittance at the level of the pile head in frequency domain is yielded. So is a semi-analytical solution for velocity response in time-domain subjected to a semi-sine exciting force. Based on the solutions proposed herein, the effects of variety of soil modulus on admittance curves and reflection wave curves are emphatically discussed. The conclusions can provide theoretical guidance for non-destruction test of piles.