<p>To investigate the mechanical characteristics, constitutive relationships, corrosion microstructure of rock-like materials under acid corrosion, specimens of cement, gypsum, quartz sand, and water were prepared in this study. Specimens were moulded and placed in pH 2 and pH 4 acid solutions for corrosion. The quality and mechanical characteristic values of specimens at different stages of corrosion at different acid solutions were determined by physiological experiment and uniaxial compression experiment. According to the properties of stress–strain curves and the strain equivalence principle, and by incorporating the microfracture Weibull random distribution statistical damage theory, taking into account the impact of the section compression density, the intrinsic formulas for rock-like materials under uniaxial compression have been derived in a segmented manner. Results show that compared to natural conditions, the modulus of elasticity and strength of acid-corroded specimens were decreased, but the peak strain was increased and brittleness was reduced. These changes were more pronounced with stronger acidity and longer corrosion. When considering the compression section, the segmented damage constitutive curve closely matched the experimental curve, validating the constitutive equation’s rationality.</p>