The high-pressure (temperature) elastic and thermodynamic properties of UO2 and UN2 is presented. For cubic UO2 and UN2, model effective interatomic interaction potential incorporating long range Coulomb, charge transfer interactions, covalency effect, Hafemeister and Flygare type short-range overlap repulsion extended up to the second neighbor ions and van der Waals interactions is formulated. Both charge transfer interactions and covalency effect apart from long range Coulomb are important in revealing high-pressure induced associated volume collapse, elastic and thermodynamical properties. The elastic constants, Debye temperature, and thermal expansion coefficient obtained are in good agreement with the available experimental data and other theoretical results. The UO2 and UN2 is mechanically stiffened, thermally softened, and ductile (brittle) in nature as inferred from the pressure (temperature) dependent elastic constants behavior. To our knowledge this is the first quantitative theoretical prediction of the pressure and temperature dependence of elastic, thermal and thermodynamical properties of UO2 and UN2 and still awaits experimental confirmation.