The structural parameters, electronic structures, and mechanical and thermodynamic properties of TaSi 2 under different pressures have been completely explored by a combination of density functional theory and quasi-harmonic Debye model. Results show that our computed structural parameters and elastic constants are in consistency with available experimental findings and previous theoretical calculations. The electronic structures of TaSi 2 under different pressures including band structures and density of states are reported. It turns out that TaSi 2 should be metallic. The elastic constants C ij , bulk modulus B , shear modulus G , Young’s modulus E , Poisson’s ratio ν, B / G , Debye temperature θ, and wave velocities under pressures are also evaluated successfully. The calculated C ij obeys the Born–Huang stability criterion, which demonstrates that TaSi 2 is mechanically stable under different pressures. More interestingly, the three-dimensional surface constructions and projections of E and B under different pressures are also systematically evaluated. With the increase of applied pressure, TaSi 2 exhibits subtle anisotropy under zero pressure, and the anisotropy strengthened. Finally, the dependence of the thermodynamic properties on pressure/temperature is obtained and analyzed for the first time.