Multi-component mass transfer in biological tissues immersed in concentrated solutions was investigated. A conceptual model was developed to represent the cellular structure of a tissue consisting of individual cells embedded in a continuous cell wall matrix. The conceptual model comprises basically two layers that represent the intracellular and extracellular volumes, and a semi-permeable membrane that separates the two layers. The concept of volume average concentration and pressure within the intracellular volume was used to represent the discontinuous properties of the concentration and pressure as a continuous function of position. A mathematical model was obtained that incorporates diffusion, bulk-flow, trans-membrane flux and shrinkage of the matrix. The conceptual and mathematical models are presented in this paper, the simulation program and the verification of the model will be presented in Part II, and the sensitivity analysis in Part III of this communication.