Abstract: The elastic and thermodynamic properties of UO2 under extreme physical condition are studied by using the density functional theory and quasi-harmonic Debye model. Results show that UO2 is still stable ionic crystal under high temperatures, and pressures. Tetragonal shear constant is steady under high pressures and temperatures, while elastic constant C44 is stable under high temperatures, but rises with pressure sharply. Bulk modulus, shear modulus and Youngs modulus increase with pressure rapidly, but temperature would not cause evident debasement of the moduli, all of which indicate that UO2 has excellent mechanical properties. Heat capacity of different pressures increases with temperature and is close to the Dulong-Petit limit near 1000 K. Debye temperature decreases with temperature, and increases with pressure. Under low pressure, thermal expansion coefficient raises with temperature rapidly, and then gets slow at higher pressure and temperature. Besides, the thermal expansion coefficient of UO2 is much lower than that of other nuclear materials.