Abstract Based on first-principles total energy calculations, we have investigated the systematic trends for structural, electronic and elastic properties of the MAX phases M 2GaN depending on the type of M transition metal (M are Ti, V and Cr). The optimized zero pressure geometrical parameters: the two unit cell lengths ( a, c), the internal coordinate z and the bulk modulus are calculated. The results for the lattice constants are in agreement with the available experimental data. The band structures show that all studied materials are electrical conductors. The analysis of the site-projected l-decomposed density of states shows that bonding is due to M d-N p and M d-Ga p hybridizations. The elastic constants are calculated using the static finite strain technique. The shear modulus C 44, which is directly related to the hardness, reaches its maximum when the valence electron concentration is in the range 10.5–11.0. The isotropic elastic moduli, namely, bulk modulus ( B), shear modulus ( G), Young's modulus ( E) and Poisson's ratio ( σ) are calculated in framework of the Voigt–Reuss–Hill approximation for ideal polycrystalline M 2GaN aggregates. We estimated the Debye temperature of M 2GaN from the average sound velocity. This is the first quantitative theoretical prediction of the electronic structures, and elastic constants and related properties for Ti 2GaN, V 2GaN and Cr 2GaN compounds that require experimental confirmation.