The first principles calculations based on density functional theory (DFT) are adopted to investigate the stability, elastic constants, Debye temperature, and hardness of MN (M = Ti, V, Zr, Nb, Ta). The NaCl-type cubic structures of MN (M = Ti, V, Zr, Nb, and Ta) compounds are optimized, and the lattice parameters are in good agreement with the experimental values. The calculated values of cohesive energy and formation enthalpy indicated that they are stable structures. The mechanical properties are presented by our calculation, which are elastic constants, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio. The Debye temperature of MN (M = Ti, V, Zr, Nb, Ta) are obtained and the results show that the value of TaN is the lowest of them. The hardness of MN (M = Ti, V, Zr, Nb, and Ta) compounds is 23.2, 25.0, 14.0, 16.0, 16.5 GPa, respectively.