Considering the 3D wave effect of soil and the kinematic soil-pile interaction, the seismic response of end-bearing single piles to vertically incident P-wave excitation is studied. The vertically incident P waves are modelled as the time-harmonic longitudinal displacement of the bedrock, and the governing equations of soil are established by considering both the longitudinal and radial displacements of the surrounding soil. The displacements of the surrounding soil are assumed as the summation of the free-field and scattered displacements, and subsequently the expression of the soil frictional force actingon the pile due to its motion is obtained. The pile is assumed to be a one-dimensional Euler bar. By substituting the soil frictional force into the governing equation of pile, the analytical solution of the seismic response of the pile under the action of vertically incident elastic P waves is obtained by considering the continuity conditions at the pile-soil interface and the boundary conditions at the top and bottom of the pile. The solution obtained is compared with existing studies to verify its validity. Finally, based on the obtained solutions, the effects of the main pile-soil parameters on the seismic amplification factor of the pile top, the kinematic response factor, the displacement of the pile, the frictional force of the soil and the kinematic Winkler parameters of the surrounding soil are investigated. The results show that: the resonance behavior of the pile-soil system occurs under the vertically incident P-waves, and the resonance behavior is particularly obvious at the first-order resonance frequency of soil layer. The pile slenderness ratio and pile-soil modulus ratio have significant effects on the seismic amplification factor of the pile top and kinematic response factor. The displacement of pile decreases significantly with the decrease of pile slenderness ratio or the increase of pile-soil modulus ratio. Compared with longer and softer piles, shorter and stiffer piles are subjected to a higher friction force of surrounding soil under seismic excitation. The influence of the pile slenderness ratio on the kinematic Winkler parameters is particularly prominent, and the kinematic Winkler parameters decrease significantly with the increase of the pile slenderness ratio, while the influence of the pile-soil modulus ratio is relatively small. The study can provide theoretical support for the seismic analysis and design of piles.