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The structural, elastic, electronic, and thermodynamic properties of ZrxNb1−xC alloys are investigated using the first principles method based on the density functional theory. The results show that the structural properties of ZrxNb1−xC alloys vary continuously with the increase of Zr composition. The alloy possesses both the highest shear modulus (215 GPa) and a higher bulk modulus (294 GPa), with a Zr composition of 0.21. Meanwhile, the Zr0.21 Nb0.79C alloy shows metallic conductivity based on the analysis of the density of states. In addition, the thermodynamic stability of the designed alloys is estimated using the calculated enthalpy of mixing. [ABSTRACT FROM AUTHOR]