The structural, electronic, optical, and elastic properties of Cu_2MgSnS_4 in four crystalline phases(wurtzite-stannite(WS), stannite(ST), kesterite(KS), and primitive-mixed Cu Au(PMCA)) are investigated using density functional theory(DFT) in the framework of the full potential linearized augmented plane wave plus local-orbitals(FP-LAPW+lo) method within the generalized gradient approximation based on the Perdew 2008 functional(GGA-PBEsol). For each phase, the structural parameters, bulk modulus, and its pressure derivative are calculated. The relative stability of these phases is also discussed. In addition, the elastic constants have been calculated in order to investigate the mechanical stability of all phases. Moreover, the anisotropy factor, shear modulus, Young’s modulus, Lame’s coefficient, and Poisson’s ratio have been estimated from the calculated single crystalline elastic constants. For the band structure, the density of states and optical properties of the exchange and correlation effects are treated by the Tran-Blaha modified Becke-Johnson potential to give a better description of the band-gap energies and optical spectra. The obtained results are compared with available experimental data and to other theoretical calculations. The structural, electronic, optical, and elastic properties of Cu_2MgSnS_4 in four crystalline phases (wurtzite-stannite (WS), stannite (ST), kesterite (KS), and primitive-mixed Cu Au (DFT) in the framework of the full potential linearized augmented plane wave plus local-orbitals (FP-LAPW + lo) method within the generalized gradient approximation based on the Perdew 2008 functional (GGA-PBEsol) The relative stability of these phases is also discussed. In addition, the elastic constants have been calculated in order to investigate the mechanical stability of all phases. Furthermore, the anisotropy factor, shear modulus, Young’s modulus, Lame’s coefficient, and Poisson’s ratio have been estimated from the calculated single crystalline elastic constants. For the band structure, the density of states and optical properties of the exchange and cor relation effects are treated by the Tran-Blaha modified Becke-Johnson potential to give a better description of the band-gap energies and optical spectra. The obtained results are compared with available experimental data and to other theoretical calculations.