Abstract: The transient wave eigenfunction method has been proposed to solve the problem of the transient dynamic response of a pile foundation with the consideration of a pile-soil-hammer interaction. Based on one-dimensional wave theory and initial-boundary conditions, analytical solutions of transient responses during impact and separation processes were obtained, respectively. The conditions of the processes that occurred alternatively were established to research on the sub-impact phenomenon. The frequencies of a pile in a numerical example were investigated during the impact process and separation process. Considering the high-frequency response excited by impact, a proper wave truncation number was suggested to choose for transient dynamic responses. Meanwhile, the propagation of transient stress waves along the pile and time history of an impact force including sub-impact process has been analyzed. The present study can provide a reference method for the pile foundation design, the selection of a hammer and the safety assessment of a system in long-term operation.