In this paper, we investigate the radial compression and inflation of a spherical shell composed of two compressible hyperelastic materials. We first establish the mathematical model of this problem as a second order nonlinear differential equation with two boundary conditions, and then transform it into a system of first order nonlinear differential equations. By using dimensionless transformation, we obtain the parametrical analytic solution. Finally, the results of the numerical simulation are given. We analyze the influence of the material parameters and the structure parameters on radial deformation of the spherical shell. These results well fit the practical phenomena.