A multiscale micro-macro numerical procedure has been developed to model the transient responses of polymeric composite shell structures. A micromechanics model which accounts for the transverse shear stress effect, the effect of strain rate dependency, and the effect of inelasticity is used for analyzing the mechanical responses of the fiber and matrix constituents. The accuracy of the micromechanics model under transverse shear loading is verified by comparison with an existing procedure. A higher-order laminated shell theory is extended to capture the inelastic deformations of the composite shell and is implemented using the finite element technique. A detailed parametric study is conducted to investigate the influence of geometry, ply stacking sequence, material models, and loading conditions on the transient response of laminated shell structures under impact loadings.