The kinetics of capillary-tissue exchange are analyzed for a cylindrical tissue region which has impermeable ends and walls (Krogh cylinder). An approximate simple analytical solution for the venous outflow curve of the general model is presented. The validity and limitations of this solution are determined by comparing it with an exact numerical solution for certain cases. The approximate solution can be used only for solutes with high capillary permeability such as D20, gasses, and small lipid soluble molecules (antipyrine). The approximate solution provides simple criteria for the validity of various simplifications of the general Krogh model and two simplified models are discussed. It is shown that the general Krogh model can be approximated by a simple one dimensional model for solutes which have a high capillary permeability. Using this approximation, it is shown that the theoretical predictions of the Krogh model do not agree with the experimental observation that the exchange of D20 in rat liver is blood flow limited.