Using First-principle calculations, we have studied the structural, electronic and elastic properties of M2TlC, with M = Ti, Zr and Hf. Geometrical optimization of the unit cell is in good agreement with the available experimental data. The effect of high pressures, up to 20 GPa, on the lattice constants shows that the contractions are higher along the c-axis than along the a axis. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The band structures show that all three materials are electrical conductors. The analysis of the site and momentum projected densities shows that bonding is due to M d-C p and M d-Tl p hybridizations. The M d-C p bonds are lower in energy and stiffer than M d-Tl p bonds. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young’s modulus and Poisson’s ratio for ideal polycrystalline M2TlC aggregates. We estimated the Debye temperature of M2TlC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Ti2TlC, Zr2TlC, and Hf2TlC compounds that requires experimental confirmation.