Abstract <p>Currently, with the dramatic increase in the number of automobiles, the problem of pavement vibration induced by vehicle travelling needs to be solved urgently. Therefore, the main objective of this paper is to develop a novel analytical computational method with the aim of analysing and solving the coupling effect and dynamic response problem of asphalt pavement vibration induced by vehicle driving. The method firstly applies the Dirac-delta function and Heaviside function to describe the car load, and constructs a car-foundation interaction model considering the friction effect by treating the foundation as a saturated-unsaturated soil layered half-space, and the asphalt pavement as the foundation surface. Secondly, the analytical solutions of each field quantity in the computational model are solved by using the triple fourier transform as well as the reduced-order method, and the accuracy is verified by comparing with the literature solutions. Finally, the discrete fourier inverse transform is used to perform the numerical inversion, and the distribution curves of each field quantity in the space and time domains are derived and analysed for the dynamic response. It is found that the enhancement of friction effect reduces the influence of longitudinal vibration displacement of asphalt pavement, while it has little effect on transverse vibration displacement. The thickness of soil layer has a significant effect on the vibration attenuation rate, and the thickness and saturation of unsaturated soil layer are the key factors affecting the vibration response of asphalt pavement. The friction effect has a small influence on the vibration frequency distribution, and the vehicle speed is the key to determine the longitudinal and transverse amplitude and frequency distribution of the ground.</p>