The structural and elastic properties of HfN and Hf-Si-N have been studied, using first principles calculations based on the density functional theory. These calculations provide the lattice parameter, cohesive energy and elastic constants of fcc (NaCl)-HfN, the N-deficient Hf-Si-N and the Hf-deficient Hf-Si-N solution phase. In order to study the relative stability, binding energy of all configurations has been calculated. The results showed that it was difficult to add a Si atom into the center of the HfN cell because the cohesive energy decreased. However, if an Hf atom or an N atom was missing in the HfN, a silicon atom was possible to occupy the vacant site and form the Hf-Si-N substitutional solid solution. Moreover, the bulk modulus, shear modulus and elastic modulus increased accordingly, the mechanical properties were improved.