Mechanical specimens of rock-like materials were prepared from cement, gypsum, quartz sand and water. After the specimens were formed, they were immersed in acid solutions of pH=2 and pH=4 for 60d and 90d respectively, and uniaxial compression tests were carried out before and after immersion to obtain mechanical parameters.Quantification of the extent of degradation of mechanical parameters and introduction of acid corrosion damage variables.Based on the Lemaitre strain equivalence principle, the Weibull distribution statistical damage model for rock-like micro-fractures was combined with a correction for damage variables that takes into account the effect of residual strength to derive a damage constitutive model under acid corrosion.The theoretical damage constitutive curves were compared with the experimental curves to analyse the applicability of the constitutive equation.The results show that after corrosion by the acid solution, the initial compression-density portion of the stress-strain curve of the specimen becomes longer and the elastic deformation phase becomes shorter,the elastic modulus, peak stress and residual strength of the specimen all decrease, and the final strain of the compression-density portion, final elastic strain, peak strain and residual strength strain values all increase,the longer the maintenance time and the more acidic the solution, the more significant the above characteristics are.Comparing the theoretical and experimental curves, the damage constitutive model, which includes acid damage and residual strength corrections, agrees well in the elastic, plastic and post-peak phases.