Elastic support is a commonly used means to the vibration isolation and the vibration reduction. Research on the dynamic response of elastically supported underground arch structures under under condition of explosive loads is of great significance for improving the battlefield survivability of personnel and equipment in underground protection projects. In this Paper, the ANSYS/LSDYNA nonlinear explicit dynamic finite element analysis program is applied to simulate the modal and dynamic response of underground arch structure with elastic support under condition of blast load, thus obtaining the low order natural frequency variation curve and the dynamic response time history curve of arch crown, arch shoulder and arch foot. The results show that the elastic support reduces the natural frequency of the structure, extends the natural vibration period of the structure, and has a good vibration isolation and vibration reduction effect. With the critical stiffness coefficient leading the first and the second modes of the structure to be easily excited at the same time, such a case should be avoided in the structural design. Compared with rigidly supported underground arches, the elastically supported underground arche is low in pressure and stress peaks, long in their appearance, good in vertical displacement peaks, and improvement in blast resistance. As for the stiffness coefficient of the elastic support, this does not mean the less the better without principle, it should be done reasonably according to the structural antiblasting capacity and ultimate displacement design requirements.