A novel finite element model based on the incremental endochronic theory with the effect of temperature was developed in this study to explore the deformed behaviors of a flexible pavement material. Three mesh systems and two loading steps were used in the calculation process for a specimen of three-dimensional circular cylinder. Computational results in the case of an uni-axial compression test for temperatures at $20^{circ}C$ and at $40^{circ}C$ were compared with available experimental measurements to verify the ability of developing numerical scheme. The isotropic response and the deviatoric response due to the thermal effect were presented from deformations in different profiles and displacement plots for the entire specimen. The characteristics of changing asphalt concrete material under a specified loading condition might be seen clearly from the numerical results, and might provide an useful information in the field of road engineering.