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The paper proposes analytical forms able to represent with very good approximation theconstitutive law experimentally deducible by means of uniaxial cyclic compressive tests on materialhaving softening post-peak behaviour in compresion and negligible tensile strength. The envelope,unloading and reloading curves characterizing the proposed model adequately approach structuralresponses corresponding to diferent levels of nonlinearity and ductility, requiring a not very high numberof parameters to be calibrated experimentally. The reliability of the model is shown by comparing theresults that it is able to provide with the ones analytically deduced from two reference models (one forconcrete, another for masonry) available in the literature, and with experimental results obtained by theauthors in the framework of a research in progress.