Using a flexible asphalt pavement structure with a graded crushed stone base is an effective means to solve reflection cracking, which frequently occurs in the semi-rigid asphalt pavements in Xinjiang. Control indicators are analyzed based on the damage form of the flexible asphalt pavement with a graded crushed stone base. Subsequently, the changing rule of the mechanical response of the pavement structure under different dynamic loading conditions is studied, which provides a theoretical basis for designing this type of pavement in Xinjiang. A 3D model with a half-sine dynamic load is built using the finite element analysis software ANSYS. Then, explicit calculation is performed using the nonlinear finite element analysis program LS-DYNA. Analysis results show that (1) tensile stress on the asphalt layer is sensitive to vehicle speed, (2) the thickness of the surface layer significantly influences shear stress on the graded crushed stone layer, and (3) the 10 cm-thick asphalt surface is an inflection point of the changing curve of the asphalt tensile stress and shear stress indicators of the graded crushed stone layer.