<p>In geotechnical engineering, physical model testing relies heavily on selecting suitable similarity materials (rock-like materials), yet traditional regression and experimental methods face limitations. This study employs statistical regression and machine learning to analyze the mechanical properties of rock-like materials. Using a Box–Behnken design, we investigate key factors (aggregate–binder ratio, cement–gypsum ratio, barite content, water content) and develop regression models. A database of mechanical properties, compiled from literature and experiments, supports a backpropagation (BP) neural network model optimized via four algorithms to predict density, compressive strength, and elastic modulus. Six models were rigorously evaluated, with the backpropagation neural network based on improved grey wolf optimization algorithm (IGWO-BP) and backpropagation neural network based on sparrow search optimization algorithm (SSA-BP) exhibiting superior performance. SHAP analysis highlights water content and aggregate–binder ratio as dominant for compressive strength and elastic modulus, while water content most influences density. The method’s broader applicability was validated through a case study on asphalt concrete fracture load (TPB test). By streamlining material design and reducing experimental costs, this work enhances efficiency in physical model testing.</p><p><b>Highlights</b><UnorderedList Mark="Bullet"> <ItemContent> <p>Aggregate–binder ratio, cement–gypsum ratio, barite content, and water content are used as parameters to build Box–Behnken design plan.</p> </ItemContent> <ItemContent> <p>Six models are trained to predict the compressive strength, density, and modulus of elasticity of similar materials used in physical model tests.</p> </ItemContent> <ItemContent> <p>The predictive performance of these models is compared and analyzed.</p> </ItemContent> <ItemContent> <p>These models are interpreted using the SHAP methods</p> </ItemContent> </UnorderedList></p>