The investigation of the mechanical properties of rock mass can be effectively carried out through rock-like material experiments. In this study, polystyrene foam particles were utilized as a novel material for simulating initial damage within rocks. Our research involved the development of sandstone-like materials with comparable mechanical properties to actual sandstone. These materials were then subjected to orthogonal mechanical tests, allowing us to identify the key factors that have a substantial impact on the mechanical parameters of sandstone-like rocks. The influencing factors considered in the orthogonal mechanical tests were the proportion of aggregate and binder, the proportion of polystyrene foam in the entire model, the proportion of binder and regulator, and the size of polystyrene foam. Five levels were set for each factor, and mechanical parameters such as compressive strength, tensile strength, elastic modulus, axial strain, and Poisson’s ratio were tested for each group of samples. The changes in mechanical parameters with the levels of the above four factors were studied. The study found that modifying the proportion of aggregate to binder can alter the elastic modulus, tensile strength, and compressive strength values of sandstone-like material. The size of polystyrene foam can be modified to alter the axial strain values of sandstone-like materials. Additionally, adjusting the ratio of binder and regulator can modify the value of Poisson’s ratio. The comparison of mechanical parameters between sandstone-like samples and sandstone reveals that sandstone-like materials can better simulate the deformation and failure mechanisms of sandstone. The error in the main mechanical parameters, such as modulus of elasticity, strength, and Poisson’s ratio, is less than 7%, indicating a greater resemblance between sandstone-like materials and sandstone. Therefore, sandstone-like materials can be used to investigate the deformation law, damage evolution law, and failure mechanism of sandstone. This can help alleviate the difficulty of obtaining specimens of deep damaged rock and the high cost of testing.