The structural and elastic properties as well as phonon-dispersion relations of the Heusler-type alloys Fe2 VAl and Fe2 VGa are computed using density functional and density-functional perturbation theory within the generalized-gradient approximation. The calculated equilibrium lattice constants agree well with the experimental values. The elastic constants of Fe2 VAl and Fe2 VGa are predicted. From the elastic constants the shear modulus, Young's modulus, Poisson's ratio, sound velocities, and Debye temperatures are obtained. By analyzing the ratio between the bulk and shear moduli, we conclude that both Fe2 VAl and Fe2 VGa are brittle in nature. The computed phonon-dispersion relation shows that both compounds are dynamically stable in the L 21 structure without any imaginary phonon frequencies. The isomer shifts in Fe in the two compounds are discussed in terms of the Fe s partial density of states, which reveal larger ionicity/less hybridization in Fe2 VGa than in Fe2 VAl. For the same reason the Cauchy pressure is negative in Fe2 VAl but positive in Fe2 VGa. © 2009 The American Physical Society.