Abstract: Based on the geomet ric nonlinear theory of the moderate-thick shallow spherical shells and the damage
theory , the constitutive relation for the laminated shallow spherical shells with mat rix damage and matrix-fiber shear damage was established by employing a st rain-based failure criterion. And a set of nonlinear equations of motion for the cross-plylaminated moderate-thick shallow spherical shells under the low velocity impact were derived. By using the orthogonal collocation point method and the Newmark method to discrete the unknown variable functions in space domain and in time domain respectively , the whole problem is solved by the iterative method synthetically. The numerical result s show that the damage , the initial velocity of the st riking object , and the shell geomet rical parameters all affect the contact force and the dynamic response of the st ructure under the low velocity impact to some extent .