Given the numerous applications of thick-walled cylinders, it is important to know the behavior of these structures. There are so many relationships for cylinders and spheres containing explosives which have been found mainly based on other experimental models. Hence derive an analytical model of the behavior of structures under internal and high-rate loading, like explosion in the cylinders, is of great importance. The main objective of this paper is to derive a mathematical model of isotropic thick-walled aluminum cylinder containing TNT in which JWL equation of state is considered for behavior of explosive expansion. The strength model the present analysis is based on the Cowper-Symonds in which strain rate at each moment is used for calculation of dynamic strength according to that. Therefore, given the instantaneous explosions pressure boundary conditions as well as instantaneous strain rate and its impact on the dynamic strength of the material, is of significant importance in this paper. With employing equations of equilibrium in thick-walled cylinders, the equations of radial and circumferential stresses and radial velocities derived. Given the instantaneous geometric and boundary conditions and correction the dynamic stress of material with respect to the strain rate, radial velocity by solving the differential equation, is calculated. After extraction of radial velocity, other stress equations will be evaluated. Furthermore, with considering the assumptions and in order to assess the overall results of the analytical modeling, computer simulation was done using Autodyn software, which shows good agreement with the analytical results.