<p>Similarity is a fundamental principle in physical analog modeling, guiding the selection of materials and experimental conditions. However, the similarity criteria for modeling the behavior of impact coal during coal burst remain underdeveloped. This study establishes a comprehensive set of similarity criteria by deriving critical parameters, such as impact stress, energy, time, and velocity, using mechanical models and similarity transformation methods. These criteria ensure consistency in the deformation and failure mechanisms of coal and rock under both static and dynamic conditions. The static similarity criterion is derived based on the Froude criterion, while the dynamic similarity criterion is investigated by varying the acceleration similarity ratio. Stress–time curves and acceleration ranges under dynamic conditions are obtained to validate the criteria. Numerical simulations further confirm the rationality of the proposed static and dynamic similarity criteria. The findings have significant practical implications. The proposed criteria enable the accurate design of physical models for simulating coal burst in laboratory conditions, facilitating a deeper understanding of coal burst mechanisms. This provides critical insights for predicting and mitigating coal burst risks in underground mining. Moreover, the methods and results can be extended to other geo-mechanical problems involving dynamic failure, such as coal burst prediction, tunnel stability assessment, and dynamic hazard control. By bridging the gap between experimental modeling and real-world applications, this study contributes to safer mining operations and improved hazard management strategies.</p>