The dynamical responses of asphalt pavement structures subjected to the vehicles are studied considering the effect of horizontal forces. Based on the elasticity, the stress distribution and deformations of asphalt pavement structures under nonaxisymmetric loads are investigated. Integral transform method is used to obtain the stress response function. And the maximum shear stress distribution and Mises stress is studied analytically and numerically. The influence of the horizontal forces and material parameters of the pavement structures on the dynamic behaviors of the structure is analyzed. The results show that the horizontal force plays important roles on the maximum shear stress and Mises stresses in structures.