The dynamic process of an underwater explosion (UNDEX) is a complex phenomenon that involves several facets. After detonation, the shockwave radially propagates at a high speed and strikes nearby structures. Subsequently, bubble oscillation may substantially damage the structures because of the whipping effect, water jet impact, and bubble pulse. This paper presents an application of explicit finite element analyses to simulate the process of an UNDEX bubble in the vicinity of rigid wall, in which the coupled Eulerian-Lagrangian (CEL) approach was developed to overcome the difficulties regarding the classical finite element method (FEM), large deformations, and flow simulation of fluid and gas. The results demonstrate that the method is well suited to manage the UNDEX bubble problem and can be used to model the major features of the bubble dynamics. Furthermore, the behavior of an UNDEX bubble near a rigid wall was also examined in the present study, which showed that the migration of the bubble and the development of the water jet are influenced strongly by the standoff distance between the initial bubble position and the wall. This method can be used in future studies to examine UNDEX bubbles in the vicinity of deformable and complex structures.