In　order　to　simulate　the　motivation　of　detonation　wave　in　the　axis-symmetry　shock　tube　with　con　verging　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.