In this study, we present the results of first principles calculations of elastic constants and phonon properties of nickel-manganese based magnetic shape memory compounds Ni2MnSn and Ni2MnSb in stoichiometric composition. The plane wave basis sets and pseudopotential method within spin-polarized generalized gradient approximation (sigma-GGA) scheme of the density functional theory is applied. In investigation of the phonon dispersion spectra, linear response technique of the Density Functional Perturbation Theory is used. Phonon softening is observed in dispersion spectra at the transverse acoustic mode (TA(2)) in [zeta zeta 0] direction as an indication of the structural instability of these systems to shear deformation. The vibrational instability of Ni2MnSb system is larger than that of Ni2MnSn yielding negative phonon frequencies. This vibrational anomaly is also verified by the low shear modulus and large elastic anisotropy ratio. The minority spin Fermi surfaces of both systems exhibit strong nesting features. (C) 2011 Elsevier B. V. All rights reserved.