In order to accurately describe the axial forced vibration law of horizontal well drill string, the paper has used the equivalent viscous damping method to linearize the Coulomb damping and established the dynamic analytical model of horizontal well drill string motion under the action of axial vibration tool after considering the continuous characteristics of drill string, Coulomb damping, viscous damping of drilling fluid and the displacement excitation of drill string by axial vibration tool, based on the continuous wave theory. The model is verified by the axial vibration tool test experiment published by Burnett et al. The influence of the frequency of the axial vibration tool and the friction coefficient between the drill string and the wellbore on the axial forced vibration of the horizontal well drill string is analyzed by numerical simulation. The results show that the axial forced vibration response of the drilling string in horizontal wells can be improved by increasing the oscillation frequency of the axial vibration tool in a certain range, and that the effect of friction coefficient between drill string and borehole wall on the axial forced vibration of horizontal well drill string decreases with the increase of drill string length. The research method and models described in this paper can be expected to provide theoretical guidance for improving the use of axial vibration tools in horizontal well operation.