The phenomenological permeation coefficients were determined for two artificial cellulose membranes of known thickness and water content. Transport of non-electrolytes was studied with tagged water, urea, glucose, and sucrose. The effect of the unstirred layers on the experimental determination of the coefficients is discussed. Frictional coefficients between membrane matrix and solutes, and between solvent and solutes in the membrane are calculated. It was shown that the geometrical tortuosity does not correspond to a physical tortuosity.