Abstract: Underground salt cavern gas storage is an important energy infrastructure, and once it is damaged by impact, it will cause irreparable losses. Therefore, it is of great significance to propose key dynamic stability indexes to evaluate the safety of salt caverns under extreme impact loads. To investigate the dynamic response of salt cavern gas storage under high-speed penetration, the salt rock material was defined using the RHT constitutive model. A finite element model of the gas storage structure was established using ANSYS/LS-DYNA software to analyze the damage effects of a ground-penetrating weapon on the salt cavern structure. Numerical simulations were conducted for three scenarios with varying overburden thicknesses, focusing on four parameters: vertical displacement, vertical stress, effective plastic strain, and shear stress. These simulations revealed the failure mechanisms of the cavern roof and surrounding rock under dynamic impact, as well as the variation patterns of key stability indicators. The results demonstrated that reduced overburden thickness intensified the dynamic response of the surrounding rock and expands plastic deformation zones. Displacements of the roof and surrounding rock exhibited an initial increase followed by a decrease. Salt rock in low vertical stress regions experienced higher shear stresses, increasing susceptibility to failure. The surrounding rock accumulated greater plastic strain, showing heightened sensitivity to penetration-induced disturbances.