In order to study the low strain numerical simulation of piles, a three-dimensional axisymmetric viscoelastic model is established. The velocity response for transient vibration is obtained by solving the 3-D wave equations. A MATLAB program is compiled via using finite difference method. The correctness and rationality of the numerical calculation are verified by comparing theoretical result with measured curve. The characteristics of velocity response at pile top are shown through analyzing the simulated results with different viscoelastic parameters. A kind of under-reamed pile (named DX pile in China) is calculated numerically while combining with the engineering practice. And the characteristics of wave propagation in DX pile are reflected intuitively in axial plane wave field diagrams. The results have a certain guiding significance for engineering practice.KeywordsThree-dimensionalViscoelastic pile–soilFinite difference methodDX pileWave field diagrams