Abstract: The common scientific foundation in the process of resource exploitation and utilization is deep rock mechanics theory. Accurately understanding the dynamic mechanical properties of deep rocks not only provides insights into the geological processes and evolution of Earth's interior, but also offers a theoretical basis for the effective extraction of deep minerals and energy. In this study, the dynamic mechanical behavior of white sandstone from a coal mine was experimentally and numerically analyzed under uniaxial, biaxial, and triaxial stress conditions. A comparative analysis was conducted using numerical simulations based on three representative constitutive models (the Riedel-Hiermaier-Thoma (RHT) model, the Holmquist-Johnson-Cook (HJC) model, and the Clay-Structure-Coupling Model (CSCM)). These simulations were validated by experimental results obtained from three-dimensional Hopkinson bar tests. The results indicate that the shear failure damage of white sandstone specimens decreases with the increasing prestress, and the damage under triaxial stress conditions is significantly lower than that under uniaxial and biaxial conditions. Among the three models, the RHT constitutive model demonstrates the closest agreement with the experimental results in terms of stress waveforms, peak stress, peak strain, and damage degree. Compared to the experimental data, the RHT model exhibits a stress peak deviation rate of 3.5% and 13.6% for the reflected wave under uniaxial and biaxial conditions, respectively, while the stress peak deviation rate for the transmitted wave is the lowest. Additionally, the peak stress and strain values predicted by the RHT model are numerically closer to the experimental results. The damage state predicted by the RHT model also aligns well with the experimental observations: under uniaxial loading, the damage exhibits a U-shaped pattern, which the HJC model shows a larger V-shaped damage pattern and fracture, and the CSCM model only displays surface damage with a smaller affected area. In terms of energy absorption and dissipation, the simulation results based on the three constitutive models shows minimal differences. The incident, reflected, and transmitted energy values are nearly identical across all three models.