This paper presents a differential model of the corneal transport system capable of modelling thickness changes in response to osmotic perturbations applied to either limiting membrane. The work is directed towards understanding corneal behaviour in vivo. The model considers the coupled viscous flows within the corneal stroma and across the epithelial and endothelial membranes. The flows within the stroma are established based on transport theory in porous media, while the flows across the membranes are described using the phenomenological equations of irreversible thermodynamics. The ability of the numerical model to reproduce corneal thickness changes in response to endothelial perturbations was tested against available experimental data. The sensitivity of the model to changes in stromal and membrane transport coefficients was examined.