An analysis to predict the transient response of a thin, curved laminated plate subjected to low velocity transverse impact by a rigid object is presented. The contact force history due to the impact phenomenon is assumed to be a known imput to the analysis. The coupled governing equations, in terms of the Airy stress function and shell deformation, are solved using Fourier series expansions for the variables. Closed-form analytical solutions for plate deflections and strains are compared with available impact test results for flat plates. Outer ply strains are used to predict fiber failures and matrix splitting between fibers in the impacted laminate.