Abstract: A frequency domain expression of shear stress along pile soil interface is derived by using Fourier transform for transient longitudinal vibration of piles.Stiffness k and damping coefficient c of the soil around the piles are obtained by applying the expression,which are functions of shear wave velocity and density of the soil,radius and vibration frequency of the pile.Good agreement between simulated and measured curves of engineering piles indicates that the expressions of k and c are very efficient for calculating transient longitudinal vibration of piles.