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Density functional theory (DFT) is applied to investigate the stability and mechanical properties of Nb x C y compounds. The structures of Nb x C y compounds are optimized, and the results are in good agreement with previous work. The calculated results of the cohesive energy and the formation enthalpy of Nb x C y show that they are thermodynamically stable structures, except for Pmc21-Nb 2 C. The mechanical properties such as the bulk modulus, Young's modulus, the shear modulus, and Poisson's ratio are obtained by Voigt-Reuss-Hill approximation. The results show that the Young's modulus and shear modulus of NbC are larger than other Nb x C y compounds. The mechanical anisotropy is characterized by calculating several different anisotropic indexes and factors, such as universal anisotropic index (A U ), shear anisotropic factors (A 1 , A 2 , A 3 ), and percent anisotropy (A B and A G ). The surface constructions of bulk and Young's moduli are illustrated to indicate the mechanical anisotropy. The hardness of Nb x C y compounds is also discussed in this paper. The estimated hardness for all Nb x C y compounds is less than 20 GPa.

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