the k-point mesh in the deformed Brillouin zone to conclude that the elastic anisotropy of the coefficient A increases as the pressure increases. Young´s modulus of Ni3Al along {100} is approximately two times higher than that along {111}. The computed elastic constants from first principles satisfy C11 › C12 › C44, which are in good agreement with the experiment data. The cubic Ni3Al possesses a bulk modulus of 312 GPa, comparable to that of cubic hafnium nitride. Theoretical calculations for Ni3Al show that all elastic moduli increase monotonically as the pressure increases. These results suggest there are potential technological applications of such materials in extreme environments.