By discretizing the pile-soil system into finite segments

the interaction of the annular projections at the interface of adjacent pile segments can be simplified as a Voigt model. The spring constant and damper coefficient of the Voigt model is then derived. Combining the displacement and stress continuity conditions at the interface of adjacent pile segments

a new relationship between impedance functions of adjacent pile segments is derived

which is called amended impedance function transfer method. Taking the transverse inertia effect into account

the pile segment is assumed to be a Rayleigh-Love rod. Taking Laplace transform on the governing equation of pile segment and combining the boundary condition at pile toe

the impedance function at pile top could be derived through the amended impedance function transfer method. A comparison study between the solution proposed in this paper and existing analytical solutions is conducted to give insight to the effects of vertical reaction of the surrounding soil on the complex impedance at pile top and velocity response at pile top subjected to transient excitation. Then a parameters study is conducted to give insight to the coupled effects between the vertical reaction of the surrounding soil and the parameters of pile-soil system on the complex impedance at pile top.