In this paper, dynamic analysis of doubly curved composite shells under low velocity impact is studied analytically. The governing equations based on the first-order deformation theory (FSDT) are derived for simply supported boundary conditions. The contact force history is predicted using two models of complete and improved spring-mass. Considering the displacement components as the doubly Fourier series, equations of motion shell and impactor are solved analytically. By writing code in Matlab softwar, using Galerkin method, the dynamic response of shell is obtained. In this investigation, the effect of geometrical parameters, such as curvature changes, aspect ratio (curvature length ratio), fiber orientation, mass and velocity of impactor, with constant impact energy, on the impact response of shell is determined by two models.