This paper investigates the vibration response of umbrella shaped tensioned membrane structure under the impact of natural disasters and other external loadings, and provides the basis for the damage analysis of actual membrane structures. Based on von Karman's large deflection theory and thin plate vibration theory, the nonlinear dynamic response control equation of umbrella shaped tensioned membrane structure under hail load is established. Bessel function and Euler equation are used to obtain the mode function, and KBM perturbation method and Galerkin method are used to solve the governing equation to obtain the approximate analytical solution of its dynamic response. The equations are solved by Mathematics software, and the data are sorted out. The time history displacement diagram of membrane surface after forced vibration is drawn by Origin drawing software. ANSYS software is used to establish the finite element model of umbrella shaped membrane structure; then, the dynamic process of hail impacting on the film surface is simulated by LS-DYNA display dynamics module, and the dynamic response of the film surface is obtained. In the same way, the displacement diagram is plotted, and the data results of the sorted theory and numerical analysis are compared and analyzed. The results show that the theoretical and numerical results are more consistent.