The structural, elastic and thermodynamic properties of thorium tetraboride (ThB4) have been investigated by using first-principles plane-wave pseudopotential density functional theory with generalized gradient approximation. The behaviors of structural parameters under 0-70 GPa hydrostatic pressure are studied by means of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) geometry optimization scheme. By using the stress-strain method, single crystal elastic constants are calculated to test the mechanical stability of the crystal structure and to determine mechanical properties such as bulk modulus at each pressure. However, in order to study the thermodynamic properties of ThB4, the quasi-harmonic Debye model is used. Then, the dependencies of bulk modulus, heat capacities, thermal expansions, Gruneisen parameters and Debye temperatures on the temperature and pressure are obtained in the whole pressure range 0-70 GPa and temperature range 0-1500 K. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.