This paper studies the transport phenomenon of solvent-penetrant systems in spherical glassy polymers. This problem involves a moving interface between a glassy region and rubbery region, the solution of which has traditionally proven very difficult. In this paper, the perturbation method is used for the complete time history of the penetrant front for a small range of perturbation control parameter a. Then, a local similarity numerical simulation is used to expand the results for a large range of epsilon. Results reveal that interface velocity near time = 0 is constant regardless of sphere dimensions, and that the interface velocity decreases after its initial constant phase, accelerating again as the interface position approaches the center of the sphere. With the proposed technique, the penetration times for different radii can be predicted.