Experiments were designed to study the role of the solvent in the transport of a solute through a solvent-swollen polymer membrane. A single solute (an organic dye), a single polymer (cross-linked natural rubber), and 24 different organic solvents were used for this purpose. The solute diffusion coefficient D was calculated from the measured permeability P and distribution coefficient K, and was compared to the diffusion coefficient of the solute in the pure solvent. The main parameters of the solvent were shown to be its viscosity and the degree it swells the polymer. At high swelling, the results are in agreement with a model that pictures the resistance to solute diffusion as hydrodynamic interaction with the solvent while the polymer acts as an obstruction that increases the tortuosity of the diffusion path. At very low swelling, the diffusion coefficient approaches an asymptotic limit which is independent of solvent viscosity. However, even with as low as 10% solvent, some effects of viscosity are still seen. These results are discussed in terms of a quantitative theory for the obstruction effect proposed by Meares and compared to other literature data.