A network thermodynamic model has been devised to describe the coupled movement of water and a permeable additive within a kidney during perfusion under the combined action of diffusive, hydrodynamic, and mechanical processes. The model has been validated by simulating perfusions with Me2SO, glycerol, and sucrose and comparing predicted weight and vascular resistance with experimental results obtained by Pegg (1993). The flows of CPA, water, colloid, and cellular impermeants are governed by a combination of the individual osmotic potential and pressure differences between compartments of the kidney, the viscoelastic behavior of the tissue, and the momentum transferred between the flows. The model developed in this study presents an analytical tool for understanding the dynamics of the perfused kidney system and for modifying perfusion protocols to minimize the changes in cell volume, internal pressure build-up, and increases in vascular resistance that currently present barriers to the successful perfusion of organs.