Full-potential computation of the electronic, magnetic, elastic and thermodynamic properties of Cu2MGa (M = Cr and V) alloys has been performed in the most stable Fm-3 m phase. The equilibrium lattice parameter is 5.9660 for Cu2CrGa and 5.9629 for Cu2VGa in the stable state. The application of mBJ potential has also found no energy gap in these alloys in either of the spin channels, hence they are metallic. The total and partial density of states, second-order elastic constants and their combinations are computed to show the electronic, magnetic, stability and brittle or ductile nature of these alloys, which are reported for the first time. Cauchy's pressure and Pugh's index predict Cu2CrGa to be brittle and Cu2VGa to be ductile. Both the materials are stiff enough to break. We have found that both the compounds are anisotropic, ferromagnetic and metallic in nature. We have used quasi-harmonic approximations to study the pressure and temperature variation of the thermodynamic properties of these alloys.