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Scientific and rational selection of rock-like materials plays a critically important role in geotechnical model tests. This study conducted physical and mechanical property tests on three types of sandstone, analyzing their microstructural characteristics and physical-mechanical behaviors. A similar material simulating sandstone, composed of cement, quartz sand, iron concentrate powder, gypsum, and pure water, was proposed. Uniaxial and triaxial compression tests were performed on specimens of this sandstone-similar material. The optimal mix proportion of the similar material was determined, and a damage constitutive model for it was established. The results indicate that the clay mineral composition of all three sandstones is dominated by quartz, feldspar, and rock fragments, with the fine-grained sandstone exhibiting the highest quartz content. The pore structure of coarse-grained and medium-grained sandstones underwent significant changes after water absorption, with their dense flaky structure becoming notably loosened, whereas the pore structure of fine-grained sandstone showed little difference after absorption. The optimal mix proportion for the sandstone-similar material was determined as follows: aggregate (quartz sand + iron concentrate powder) accounting for 70% of the solid mass (quartz sand + iron ore concentrate + cement + gypsum), the aggregate component ratio (quartz sand : iron ore concentrate) being 2:1, the binder component ratio (cement : gypsum) being 1:0, and a water mixing ratio of 25%. A strain-softening damage statistical constitutive model for the sandstone-similar material was established, and verification shows that this model accurately reflects the stress-strain relationship of the material under triaxial compression conditions.