First-principles calculations of the crystal structure and the elastic properties of tetragonal WN₂ have been performed with the plane-wave pseudopotential density functional theory method. The calculated structural parameters and elastic constants at zero pressure and temperature are in excellent agreement with the available theoretical results. The dependence of the elastic constants C_ij, the aggregate elastic moduli B, G and the anisotropies on pressure have been investigated. WN₂ is a brittle system below about 66 GPa, whereas it becomes ductile under high pressure. By the elastic stability criteria, it is predicted that tetragonal WN₂ are not stable above 232.1 GPa.