Abstract: The response of flat spherical shell is studied under local impact by a projectile. Firstly, the model of deformation energy of the flat spherical shell is improved based on the available dynamic theoretical research on spherical shell and the assumption of rigid-plastic material. The energy associated with dimple deformation and membrane deformation in the ridge is considered only. The theoretical result of spherical shell is obtained under impact loading according to the law of energy conservation. Next, the approximate relationship, i.e. l≈0.05a between radius of the dimple and width of the ridge is introduced and the explicit approximate theoretical solution of the shell is given under the impact of low velocity. Then, a comparison is made between the theoretical and experimenta1results, which indicates that the relative errors are less than 10%. Finally, a simulation is carried out using finite element software LS-DYNA. The numerical results are in good agreement with the corresponding approximate theoretical ones.