Abstract: This paper introduces the modeling of the vertical pile response from time-domain wave equation analysis with the soil spring constants derived from t-z and Q-z curves and the time-dependent damping coefficients obtained from the dynamic impedance functions. The pile displacements under various loads were simulated efficiently, and they are highly dependent of the soil-pile interface model used. The major difference between this solution and others appears to be the pile-head displacements under monotonic load and the attenuation of displacements under impulsive load. Calibrating the parameters in the damping model and soil spring can minimize the deviations. By correcting the soil spring constant, the model can be used to obtain the design curves of pile displacements and to match the experimental data of in situ pile load tests.