Abstract: In order to simulate the motivation of detonation wave in the axis-symmetry shock tube with converging cross-sections,we use an explicit finite element scheme for nonlinear multi-dimensional hyperbolic conservation laws,and obtain satisfactory computing results.The scheme is uniformly guarantees nonlinear stability,which is suitable for solving convection dominated problems and providing continuous solutions to nonlinear multi-dimensional hyperbolic conservation laws.In the numerical simulation of detonation wave,the idea to deal with the argument γ and the state equation is creative and the scheme can be used in the scientific computing on a large scale.