First-principles density functional theory based calculations have been used to predict the bulk mechanical properties of magnetic shape memory Heusler alloy Ni2MnGa substituted by copper (Cu), platinum (Pt), palladium (Pd) and manganese (Mn) at the Ni site. The elastic constants of Ni2MnGa alloy with and without substitution are calculated. We analyze and compare in detail the bulk mechanical properties for these alloys, in particular, the ratio between the calculated bulk and shear modulii, as well as the Poisson's ratio and Young's modulii. This analysis further based on an empirical relation, indicates that Pt2MnGa may inherently be the least brittle material, among the above-mentioned alloys. Interesting difference has been observed between the shear modulii calculated from Voigt's and Reuss's method. This has been explained in terms of the values of the tetragonal shear constant C' of the materials. Study of Heisenberg exchange coupling parameters and Curie temperature as well as density of states of the materials shows the effect of substitution at the Ni site on the magnetic and electronic properties, respectively. (C) 2015 Elsevier B.V. All rights reserved.