The objective is to study the perforation of a plastic spherical shell impacted by a cylindrical projectile. First, the deformation modes of the shell were given by introducing an isometric transformation. Then, the perforation mechanism of the shell was analyzed and an analytical model was advanced. Based on Hamilton principle, the governing equation was obtained and solved using Runge-Kuta method. Finally, some important theoretical predictions were given to describe the perforation mechanism of the shell. The results will play an important role in understanding the perforation mechanism of spherical shells impacted by a projectile.