To give guidance for developing Rh-based superalloys, systematic investigations on structural, elastic and thermodynamic properties of Rh and Rh3Zr are conducted by first-principles calculations. The pressure dependence of the basic mechanical parameters is presented covering elastic constants, bulk modulus, shear modulus, Young's modulus, Poisson's ratio, aggregate sound velocities and elastic anisotropy. Additionally, the mechanical stability and ductility/brittleness are also assessed. Compared with Rh, it is found that Rh3Zr has higher ductility but lower elastic moduli, lower aggregate sound velocities and higher elastic anisotropy. The variations of the thermal properties including the normalized volume, bulk modulus, thermal expansion coefficient and heat capacity of Rh and Rh3Zr in wide pressure (0-40 GPa) and temperature (0-2200 K) ranges are also predicted and analyzed, and a remarkable consistency with experimental results is obtained. (C) 2014 Elsevier B.V. All rights reserved.