Using ab initio calculations, we have studied the structural and elastic properties of M 2 InC , with M = Sc , Ti , V , Zr , Nb , Hf and Ta . Geometrical optimization of the unit cell is in agreement with the available experimental data. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M 2 InC aggregates. We estimated the Debye temperature of M 2 InC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Sc 2 InC , Ti 2 InC , V 2 InC , Zr 2 InC , Nb 2 InC , Hf 2 InC and Ta 2 InC compounds, and it still awaits experimental confirmation.