Abstract: The mechanics models were established for arches with flexible supports at their ends. The flexible supports include vertical elastic and damping supports, horizontal elastic supports, and rotatable elastic supports. Based on the large deformation dynamic differential equations and finite difference method, the dynamic responses of arches subjected to explosive loading were explored, and the effects of flexible supports on explosion resistant capabilities were analyzed. The analysis shows that flexible supports have great effects on explosion resistant capabilities of arches, and different supports have distinctly different influences. Vertical elastic supports can decrease the peak internal forces of arches under explosive loading, postpone the appearance times of the peak internal forces, and improve the bearing capabilities of arches to explosive or transient loading. But horizontal elastic supports can increase the peak internal forces and relative displacements of arches, and weaken the bearing capabilities of arches.