First-principle calculations on the structural, electronic, optical, elastic and thermal properties of the chalcopyrite $\rm{MgXAs_{2} (X = Si, Ge)}$ have been performed within the density functional theory (DFT) using the full potential linearized augmented plane wave (FP-LAPW) method. The obtained equilibrium structural parameters are in good agreement with the available experimental data and theoretical results. The calculated band structures reveal a direct energy band gap for the interested compounds. The predicted band gaps using the modified Becke–Johnson(mBJ) exchange approximation are in fairly good agreement with the experimental data. The optical constants such as the dielectric function, refractive index, and the extinction coefficient are calculated and analysed. The independent elastic parameters namely, $C_{11}, C_{12}, C_{13}, C_{33}, C_{44}$ and $C_{66}$ are evaluated. The effects of temperature and pressure on some macroscopic properties of $\rm{MgSiAs_{2}}$ and $\rm{MgGeAs_{2}}$ are predicted using the quasiharmonic Debye model in which the lattice vibrations are taken into account.