First,the knowledge of mechanics and electromagnetics was applied to build the equilibrium equation of thick-walled cylinders' structures,and a solvable equation was obtained utilizing the Laplace transforms and the Hankel integral transforms.Then, we presented an analytical method to solve the dynamic stresses and perturbation of magnetic field vector under thermomagnetic shock,and obtained the response histories and distributions of the dynamic stresses and the response histories of perturbation of magnetic field vector.Finally,some practical examples were used to test the method,and it proved that the method was simple and effective.