Mass transfer in heterogeneous materials is the topic of this chapter. This chapter follows on the concepts developed in Chapter 5 with specific applications to mass transport in membranes. Steric exclusion and hindered diffusion of the solute in the pores of a membrane are described along with the Renkin equation. The solute membrane permeability is also developed. The analytical solution describing the unsteady diffusion of a solute in a porous material is given along with the special cases of short and long contact time solutions. The special case of solute diffusion in blood and tissue is also provided. There is also a discussion on solute transport by both filtration and diffusion. The Krogh tissue cylinder model is then presented to describe solute transport between a capillary and the surrounding tissue. This model is then simplified to give the Renkin-Crone equation, which can be used to find the capillary solute permeability.