Using ab initio calculations, we have performed a study of the hydrostatic
pressure effect on the equilibrium volume, lattice parameters, elastic
modulus, and elastic anisotropy of selected M2AlC phases with M = Ti, V,
Nb, and Ta. The deviations of our calculated volume change are lower than
3% comparing with experimental measurement, lead to a discrepancy in the
bulk modulus less than 15%. Our results show a linear pressure dependence
of the elastic modulus and the bulk modulus. Shear elastic anisotropy factor
increase with the pressure enhancement, while the compressibility anisotropy
remains constant around weak values.