The first principles calculations based on density functional theory (DFT) were performed to investigate the stability, the chemical bonding, the elastic constants, the hardness and the Debye temperatures of M3B2 (M=V, Nb and Ta). The structures of these borides were optimized, and the lattice parameters are in good agreement with the experimental values. The calculated cohesive energy and the formation enthalpy indicate that they are thermodynamically stable structure. The mechanical properties including elastic constants Cij, bulk modulus, young’s modulus, shear modulus and Poisson’s ratio were calculated. The Debye temperatures of M3B2 (M= V, Nb and Ta) were calculated. The results show that the values of M3B2 range from 299 to 526 K. The hardness of M-B bonds was calculated using a semi empirical hardness theory.