AbstractThe interaction between a soil layer and an end bearing pile in vertical vibration induced through the frictional interface is theoretically investigated. The pile is assumed to be vertical and elastic, whereas the soil is considered as a linear visco‐elastic layer with hysteretic damping. Slip between the pile and the soil is allowed to occur along the frictional interface, in which the hysteretic frictional stress is linearized to permit modal decomposition. Approximate solutions of the pile and the soil for steady‐harmonic loads are obtained in closed form by composing the wave modes of the layer. The displacement amplitudes of the pile and the soil, the critical slip force, the stiffness of the pile head, and the modal stiffness contribution of the soil to the pile are evaluated numerically with respect to the ratio of applied force level to the slip stress level and the slenderness ratio, at various frequenc