While the dynamic response of a variety of structures subjected to underwater explosion (UNDEX) has been studied for decades, investigations of the damage and failure of reinforced concrete (RC) structures are lacking. Here we present the results of a comprehensive computational study of the dynamic response of air-backed RC slabs exposed to UNDEX. To determine the loading produced by the explosion, a model involving parameters associated with the equations of state for water and explosive was validated by comparing its predictions with UNDEX experiments on a steel plate conducted in a centrifuge. This loading was then used to predict the response of an air-backed RC slab under UNDEX. Damage and failure of the RC slab were simulated using both continuum damage mechanics and peridynamics. The results of the two methods were consistent with each other and offer promise for assessing the damage experienced by RC slabs that are subjected to UNDEX.