The commonly used shrinking core model (SCM) envisages a sorbing species to diffuse through a particle as a sharp inward-moving front separating a completely untouched core ahead of the front from a completely saturated shell behind the front. However, in many situations involving the uptake of water soluble species onto sorbent particles and ion exchange resins, the assumption of a completely saturated shell may not be justified. The objective of this communication is to derive a model that generalizes the SCM to allow for an incompletely saturated shell. As with the SCM, the advance of the sorbate into the particle is marked by a distinct interface moving inward with a velocity dictated by the interplay between the rates of diffusion and uptake onto the solid matrix. Local equilibrium is considered to exist between the diffusing sorbing species in the pore space and the form bound to the matrix, as with many homogeneous models such as the linear absorption model (LAM). The model is general enough to accommodate any function describing this local equilibrium. We show that this model simplifies to the conventional SCM as a special limiting case. As an example, the model is applied to previously reported data for the uptake of Cu 2+ ions onto calcium alginate gel beads and shown to fit well, comparable to that obtained previously using the SCM and LAM. However, the predicted concentration profiles within a particle during sorption are shown to vary markedly depending on the model.