A comprehensive theoretical study of the structure, electronic, optical, and elastic properties of ternary semiconductor silver thiogallate crystal AgGaS2 is carried out based on the density functional theory and dipole electron shifting model (DES) for finding a structure–properties relationship. The deformation and displacement parameters, describing the deviation of the structural parameters of AgGaS2 from ideal chalcopyrite structure, are determined. It is noticed that the significant discrepancies concerning peculiarities of the band structure between initial results of the DFT‐based calculation and the experiment for the titled crystal have been efficiently eliminated by choosing the proper DFT + U approach. By utilizing the calculated dielectric function for two principal directions, the refractive indices and extinction coefficients dispersions are determined. For the first time, the linear electro‐optic properties, electrogyration coefficients, and second‐order nonlinear optical coefficients of AgGaS2 crystals are calculated in the frame of the DES model. The elastic properties of the AgGaS crystal are analyzed in the frame of the calculated full matrix of elastic coefficients. A number of parameters, such as Young's modulus E, Poisson's ratio ν, bulk B, and shear G moduli are predicted for the crystal. The calculated anisotropy coefficients for the moduli show very good agreement with ones available from experiment.