As a common structure in engineering, reinforced concrete (RC) arch may be subjected to explosion load in its life cycle. However, there are few studies on the blast resistance of RC arch against underwater explosion. A normal strength reinforced concrete (NSRC) arch and a high strength reinforced concrete (HSRC) arch were designed, and two sets of underwater explosion tests were carried out. Multi-media coupling models of the two RC arches subjected to underwater explosions were established based on the Arbitrary-Lagrangian-Eulerian (ALE) algorithm. The propagation characteristics of shock wave, the acceleration response and damage evolution of the arches were experimentally and numerically investigated. The reliability of the numerical method was verified by comparing the numerical results with the test results. Employing the verified numerical method, the effects of standoff distance and explosive weight on the dynamic response and damage distribution of the NSRC and HSRC arches were further studied. Based on extensive numerical simulations, the prediction formulas for the peak displacement of the given NSRC and HSRC arches due to specific underwater explosions were proposed. The results show that the arch vault and both sides of hance are the most vulnerable to failure when suffering the explosions centrally above the arch. The blast resistance of the HSRC arch is much stronger than that of NSRC arch. The failure modes of RC arches can be summarized as: arch vault cracking, global bending failure, combination of global bending failure and local damage, combination of global bending failure and penetration failure.