Abstract: The dynamic interaction between pile and pile around soil was described by Winkler springdamping, and the stiffness and damping coefficients of the pile around soil were obtained. By considering the continuous conditions of the embedded part and exposed part of pile, the lateral vibration of partially embedded end bearing friction pile in fractional derivative viscoelastic soil was solved with transfer matrix method, and the dynamic impedance at pile head were obtained. The influence of the order of fractional derivative, length of exposed part of pile and constitutive model parameters on the lateral vibration of pile were investigated. It is shown that the order of fractional derivative and the constitutive model parameters had a certain influence on the horizontal dynamic stiffness, but had little influence on the equivalent damping, and the length of exposed part of pile had great effect on the horizontal dynamic impedance of the pile