In order to solve the underwater explosion flow field with large discontinuities, Level Set method was applied to track the interface position of the multi-medium flow, Ghost Fluid method was used to calculate the physical parameter of both sides of the interface, time and space were discretized by Runge-Kutta Discontinuous Galerkin Method, Euler equations of the flow field were solved. One-dimensional and two-dimensional assessments were conducted by RKDG approach. The results reflect the phenomena of underwater explosion shock wave generation, propagation, reflection and explosion products expansion. Finally, the shock responses and damage characteristics of hull plates under shock load were simulated with the nonlinear FEM softeware ABAQUS. The RKDG method can be applied to simulate the hull plates response with high accuracy. The response of hull plates is inversely proportional to the blast center distance.