The full-potential linearized augmented plane wave (FP-LAPW) method, based on the density functional theory (DFT) with the generalized gradient approximation (GGA) plus modified Becke-Johnson (mBJ), are used to study the structural, elastic, electronic, and optical properties of Na₂SrX (Si and Ge) full-Heusler alloys. Our calculations indicate that the studied compounds have a nonmagnetic Hg₂CuTi structure. Calculations of electronic band structures and the densities of states showed that Na₂SrSi and Na₂SrGe compounds exhibit semiconductor behaviour at optimized equilibrium lattice constants, with indirect band gaps along the L–X direction of 0.652 eV and 0.629 eV, respectively. The exciton binding energy in the Wannier-Mott model was found to be 8.58 meV for Na₂SrSi and 6.91 meV for Na₂SrGe. We show that these compounds exhibit dynamic and elastic stability. Moreover, the formation energy suggests that these compounds can be synthesized experimentally. Besides, the optical properties (complex dielectric function, refractive index, reflectivity, and optical absorption) were also examined. The results obtained suggest the potential of these full-Heusler alloys for optoelectronic devices in the ultraviolet range.