Two mathematical models to describe the loading of ion-exchange resin beads following shell-core behaviour under finite bath conditions are developed. An analytical solution is obtained for the model based on a simplifying assumption of quasi-steady state diffusion, while the model on non-quasi-stationary diffusion is converted by finite integral transform to a system of first order differential equations, which are then solved by numerical means. The two models, tested with sorption data of aqueous sulphur dioxide on cross-linked poly(4-vinyl pyridine) resin Reillex(TM) HP measured under finite bath conditions, yield comparable results.