We have investigated the structural and elastic properties of ZrC under high pressures using the norm-conserving pseudopotentials within the local density approximation in the frame of density-functional theory. The calculated pressure dependence of the normalized volume is in excellent agreement with the experimental results. The (a - a(0))/a(0), (V - V-0)/V-0, the ductile/brittle, the elastic constants C-ij (GPa), shear modulus C', bulk modulus B, shear modulus G (GPa), Young's modulus E (Gpa), Poisson's ratio sigma and anisotropy factor A as a function of applied pressure are presented. Through the quasi-harmonic Debye model, we also study the thermodynamic properties of ZrC. The thermal expansion versus temperature and pressure, the thermodynamic parameters X (X. Debye temperature or specific heat) with pressure P, and the heat capacity of ZrC at various pressures and temperatures are estimated. (C) 2009 Elsevier B.V. All rights reserved.