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The structure and mechanical properties of tantalum mononitride (TaN) are investigated at high pressure from first-principles using the plane wave pseudopotential method within the local density approximation. Three stable phases were considered, i.e., two hexagonal phases (e and h) and a cubic d phase. The obtained equilibrium structure parameters and ground state mechanical properties are in excellent agreement with the experimental and other theoretical results. A full elastic tensor and crystal anisotropy of the ultra-incompressible TaN in three stable phases are determined in the wide pressure range. Results indicated that the elastic properties of TaN in three phases are strongly pressure dependent. And the hexagonal h-TaN is the most ultraincompressible among the consider phases, which suggests that the h phase of TaN is a potential candidate structure to be one of the ultraincompressible and hard materials. By the elastic stability criteria, it is predicted that h-TaN is not stable above 53.9 GPa. In addition, the calculated B/G ratio indicated that the e and d phases possess brittle nature in the range of pressure from 0 to 100 GPa. While h phase is brittleness at low pressure (below 8.2 GPa) and is strongly prone to ductility at high pressure (above 8.2 GPa). The calculated elastic anisotropic factors for three phases of TaN suggest that they are elastically highly anisotropic and strongly dependent on the propagation direction.

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