An analytic solution is given for the problem of simply-supported orthotropic cylindrical shells subject to impact loading. The closed-form solution has not been obtained previously. The analysis is based on an expansion of the loads, displacements, and rotations in a double Fourier series which satisfies the end boundary conditions of simple support. Each expansion is assumed to be separable into a function of time and a function of position. By neglecting in-plane and rotary inertia the problem becomes a second-order ordinary differential equation in time for the Fourier coefficients of the radial deflection. For a given loading impulse the solution can be found by invoking the convolution integral. The results show that for impact by a heavy mass, the solution is equivalent to that obtained by an approximate procedure of neglecting the mass of the shell, which leads to a simple simple-degree-of-freedom analysis. For problems of impact by smaller masses, the higher response frequencies of the cylinder become important. The results show the importance of dynamic effects in the predicted impact duration, peak force, and peak deflection relative to the quasi-static response. The results show that the response amplitude varies linearly with the impact velocity, but the response characteristics depend on the mass of the impactor and the mass and stiffness of the cylinder.