Tc and its nitrides TcN, TcN2, TcN3 and TcN4 are studied using the projector augmented wave method based on the density functional theory. The elastic properties, electronic structure and atomic populations, theoretical hardness of Tc nitrides are calculated and analyzed. The calculation results show that with increasing N content by incorporated into transition-metal Tc, the solid structures of the material change into laminar, and its elastic moduli do not monotonically increase. It reveals that TcN with solid structure has the largest bulk modulus and the smallest shear modulus, while TcN3 with layered structure has the largest shear modulus and the smallest bulk modulus, and TcN4 is found to have the largest theoretical hardness by means of chemical bonding analysis. It can be seen that the bulk modulus depends mainly on electrons per atomic volume and mass density, while covalent structure of chemical bonding and N content make more contribution to theoretical hardness, and appropriate content N—N covalent bonding in the same direction tends to increase the shear modulus of nitrides.