Abstract: The nonlinear dynamic buckling for laminated composite shallow spherical shells, which include transverse shear deformation, under the action of explosive impact was investigated. By means of the basic equations of nonlinear buckling for laminated composite shallow spherical shells,and adding the transverse inertia term and introducing the explosive load of R.H.Cole theory, the nonlinear dynamic governing equation for laminated composite shallow spherical shells subjected to explosive impact load was gained.The nonlinear dynamic responsive equation was obtained by Galerkin method and solved by Runge-Kutta method. Budiansky-Roth motion criterion expressed by peak displacement was employed to determine the critical explosive impact buckling load. The effects of geometric parameters on dynamic buckling of laminated composite shallow spherical shells were discussed. Numerical results show feasibility of the Galerkin Method.