To reduce the damage of earth penetrators on underground fortifications against blast and fragmentation penetration, a model of underground arch structure with elastic support was established for a modal analysis on the structure subject to penetration and explosion with ANSYS/LS-DYNA software for dynamic analysis. In the process, the effect of spring stiffness coefficient on the dynamic response of the structure was analyzed in terms of pressure, equivalent stress, and peak vertical displacement. The simulation results showed that the elastic support reduced the dynamic response of the structure, while the equivalent stress and pressure of each part of the underground arch structure were reduced, and the peak vertical displacement was increased as the stiffness coefficient of the elastic support was lowered, and the isolation efficiency of equivalent stress and pressure at the arch shoulder was lower than that at other parts. Therefore, reducing the stiffness coefficient of the elastic support alone cannot meet the need for vibration isolation of the arch shoulder, and the type or stiffness coefficient of elastic support should be selected reasonably according to the actual engineering requirements, so as to achieve a good vibration isolation effect.