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