The structure and properties of three layered heterometallic quaternary sulfides SrLaCuS3, SrNdCuS3 and SrTmCuS3 were studied for the first time using first-principles calculations in the stoichiometric and nonstoichiometric approximations. The applied DFT-based computations were performed using a hybrid functional with the contribution of nonlocal exchange in the Hartree-Fock formalism. It was revealed that the nonstoichiometry of SrLaCuS3 and SrNdCuS3 must be considered for modeling phonon spectra, elastic properties and band gaps. The wavenumbers and types of the Raman and “silent” modes at the Г-point were determined. From the analysis of displacement vectors, the degree of participation of ions in each mode was determined. The elastic constants and elastic moduli of the reported sulfides were calculated. © 2024 Elsevier B.V.