Density functional theory (DFT) calculations are performed to investigate the structural, electronic, magnetic, and elastic properties of Ni2MnZ (Z = B, Al, Ga, In) and Ni2FeZ (Z = Al, Ga) full Heusler alloys. The alloys are found to be metallic ferromagnets with total magnetic moments of about 4μB/f.u. and 3μB/f.u for Ni2MnZ and Ni2FeZ alloys, respectively. The Ni2MnAl and Ni2MnIn alloys are found to be stable at L21 phase, while the other alloys are more stable in the tetragonal phase with c/a ratios of 1.38 and 1.27 for Ni2MnB and Ni2MnGa, respectively and 1.35 for both Ni2FeAl and Ni2FeGa. The Ni2MnB alloy exhibits the highest electron spin polarization in its tetragonal phase, which is about 88% greater than that of L21 structure. However, the Ni2MnGa, Ni2FeAl, and Ni2FeGa alloys exhibit lower spin polarizations in their tetragonal phase than those at the L21. The most contribution of the total magnetic moments comes from Mn or Fe atoms, whereas Ni atoms exhibit much smaller magnetic moments. However, Z atoms have small induced magnetic moments, which are coupled antiferromagnetically with Ni, Mn and Fe.