The structural, electronic, anisotropic elastic, and lattice dynamical properties of the M(2)AB (M = Ti, Zr, Hf; A = Al, Ga, In) compounds belong to the family of MAX phases have been investigated by accomplishing the first principles density functional theory (DFT) calculations with utilizing the generalized-gradient approximation (GGA). Structural parameters, formation enthalpies, and X-ray diffraction patterns have been calculated for all compounds. Electronic band structure and corresponding density of states (DOS) have been obtained. Having negative formation enthalpy showed that, all compounds could be experimentally synthesized. Also, among the nine different M(2)AB compounds, the most stable one has been found as Hf2InB with respect to the formation enthalpies and band filling theory calculations. Moreover, the elastic constants have been predicted using the stress-finite strain technique. The numerical estimations of the bulk modulus, shear modulus, Young's modulus, Poisson's ratio, Pugh's modulus, hardness, thermal conductivities, and anisotropy factors have been studied. All compounds are found to have low thermal conductivity and all compounds (except Zr involved ones) are hard materials and mechanically stable. Furthermore, the phonon dispersion curves as well as corresponding phonon PDOS have been plotted. (C) 2017 Elsevier B.V. All rights reserved.