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Abstract: We have performed first principles full-potential augmented plane wave plus local orbitals (FP-APW+lo) calculations within the local density approximation (LDA) and the generalized gradient approximation (GGA), with the aim to determine and predict the elastic constants and their pressure dependence for the alkali-metal sulfides Li2S, Na2S, K2S and Rb2S. The ground state properties are found to agree with the experimental and other theoretical results. The calculated elastic constants at zero pressure for Li2S and Na2S are compared with the available experimental data and other theoretical results. With regard to K2S and Rb2S, we are not aware of any experimental or theoretical data for the elastic constants and their pressure dependence, so that the data here represent the first determination of these quantities. The shear modulus, Young’s modulus and the Poisson’s ratio for these compounds are derived. The Debye temperature is also estimated from the average sound velocity. [Copyright &y& Elsevier]