In this study, the differential quadrature method (DQM), a mathematically simple, accurate, and computationally efficient numerical tool, was employed to analyze the response of single piles under dynamic axial loading. The dynamic behavior of the piles and surrounding soil were modeled using the one-dimensional (1D) or three-dimensional (3D) axisymmetric elasticity theory, respectively. The governing equations subjected to the related boundary and initial conditions were discretized in both the spatial and temporal domains via DQM. The behavior of the floating piles embedded in a half-space layer of homogeneous and Gibson soils under uniform and sinusoidal impact loads was studied. The piles and the soil behavior were assumed to be linear elastic and linear viscoelastic, respectively. To compare and verify the results obtained from the DQM approach, the problems were also solved via a finite-element-based commercial software program in some cases. The approach was found to have high accuracy and numerical stability. Finally, the effects of the different parameters of the soil and pile on the pile-head settlement time history were investigated.