This paper introduces a time-dependent radiation damping for the time-domain wave equation analyses of single piles. By deriving the radiation damping ratios of the linear viscoelastic soils along the pile from the dynamic impedance functions (Novak, 1974), time-dependent damping coefficients are obtained from the inverse Fourier Transform of these damping ratios and the static soil spring constants. Numerical examples are studied by solving the wave equations with the finite difference scheme. Applications of the modeling are presented and discussed with emphasis on identifying the primary factors that control the performance of piles. It is important to know that this solution, in contrast to the ordinary frequency-domain approach, can predict the softening load-displacement response of the piles under cyclic loads. The pile response under monotonic loads would be significantly influenced by the proposed damping parameters.