All piezo-optic coefficients (POCs) and elasto-optic coefficients (ELOCs) of Ca3NbGa3Si2O14 (CNGS) and Ca3TaGa3Si2O14 (CTGS) trigonal crystals of the langasite group are determined from quantum mechanical calculations based on the hybrid density functional theory, as implemented in the CRYSTAL program. The calculation results for CTGS crystals are compared with experimental data. Indicative surfaces of piezo- and elasto-optic effects are constructed based on the POC and ELOC matrices of CNGS crystals and the largest values of these effects are determined. The maximum values of the coefficient of the acousto-optic figure of merit M2 of the CNGS crystal are determined for the geometries of elasto-optic interaction, which correspond to the maxima of the elasto-optic effect. These results are compared to the corresponding results for CTGS and langasite crystals. The spectral dependence of the POCs and ELOCs of CNGS and CTGS crystals on the light wavelength is investigated in the 600–1500 nm range.