A mathematical analysis of the exchange of fluid between a blood capillary and the surrounding tissue is presented. The diameter and permeability of the capillary are assumed to vary along its length in accordance with observation, and fluid movement across the capillary wall is assumed to be governed by a generalization of Starling's law. The motion of the interstitial fluid obeys a non-linear form of Darcy's law in which the porosity and hydrodynamic conductivity of the tissue varies with interstitial fluid pressure. An asymptotic method of solution is developed for a simplified problem in order to establish techniques applicable to the general case. The results are used to discuss some specific examples of physiological interest.