The problem of diffusion and heat conduction in two-phase systems is used to illustrate the utility of approximate solutions for the closure problem associated with the method of volume averaging. Numerical solutions for spatially periodic models are compared with experimental data and with an approximate solution of the closure problem first used by Chang. Chang’s unit cell replaces the spatially periodic boundary conditions in the closure problem with a Dirichlet condition that leads to analytical solutions for the closure variables. These analytical solutions are identical to the classical solutions of Maxwell and Rayleigh, and the comparison between spatially periodic models and Chang’s unit cell indicates only minor differences between the two approaches. In this work we extend the studies of Chang to include both interfacial resistance and anisotropic systems which are generated by means of ellipsoidal unit cells. The inclusion of interfacial resistance is important for the study of diffusion in cellular systems, while the use of ellipsoidal unit cells provides a comparison between theory and experiment for diffusion in anisotropic porous media.