The results of first principles calculations of the structural parameters, elastic moduli, electronic structure and optical properties of the ternary rhombohedral layered compounds AEuS2 (A = Na, K, Rb and Cs) are reported. These calculations were performed by employing the Linear Combination of Atomic Orbitals (LCAO) method. The calculated structural parameters using different exchange and correlation approximations are in good agreement with the experimental data, and the best agreement is obtained with the PBE0 functional. The mechanical stability of the AEuS2 compounds is investigated for the first time by calculating the single‐crystal elastic constants Cij using the stress–strain approach; and the macroscopic elastic parameters, such as the bulk modulus β and shear modulus G, were determined by using Voigt–Reuss–Hill approximations (VRH). Electronic properties have been studied through calculation of band structure and density of states. It is shown that these crystals belong to the semiconductors with an indirect band gap. Furthermore, in order to investigate the optical transitions of these compounds, linear optical functions such as the complex dielectric function, optical reflectivity and loss function were computed for an energy range from 0 to 20 eV. The calculated optical spectra show the anisotropic nature of the optical properties of the AEuS2 (A = Na, K, Rb, and Cs) compounds.