We have performed ab‐initio density‐functional theory self‐consistent calculations using the full‐potential linear muffin‐tin orbital method within local spin‐density approximation to study the electronic and magnetic properties of Ni2MnZ (Z = Al, Ga and In) in L21 structure. The magnetic phase stability is determined from the total energy calculations for both the nonmagnetic (NM) and magnetic (M) phases. The theoretical calculations clearly indicate that at both ambient and high pressures, the magnetic phase is more stable than the nonmagnetic phase. The elastic constants at equilibrium are also determined. We derived the bulk and shear moduli, Young's modulus, and Poisson's ratio. The Debye temperature of Ni2MnZ was estimated from the average sound velocity. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)