Abstract: The steady-state amplitude-frequency response curve for the primary resonances of the nonlinear axial forced vibration of a pile fixed at one end and free at the other end is presented by the method of multiple time scales. Results show that the amplitude-frequency response curve for the nonlinear axial forced vibration of the pile is related to not only the natural frequency of the derivational linear vibration system, soil rigidity, and damping coefficient, but also the amplitude, phase and nonlinear eigenvector. A kind of typical nonlinear phenomenon of amplitude skipping is appeared on the amplitude-frequency response curve. When the exciting frequency approachs to the natural frequency of linear system, the system produce resonance so as to increase the response amplitude, and one exciting frequency is corresponding to several different values, and the motion state has instability. As the nonlinear coefficient increases, the peak of response curve bends to the left; viscous damping could restrain the accretion of responding amplitude; the accretion of incentive amplitude results in the accretion of responding amplitude.