Capillary flow affects the amount of air entrapped between fiber reinforced composites during the impregnation. This paper investigates the permeability of aligned fiber bundles by capillary flow in both longitudinal and transverse directions. Experiments measure capillary flow by the rate of weight gain of fiber-filled tubes having one end in contact with a fluid at atmospheric pressure. The driving force for this flow is capillary pressure only; no external driving pressure is applied during impregnation. Permeabilities obtained under these conditions are slightly lower than those measured under conditions of positive external pressure. The Kozeny constant for longitudinal flow are found to be 1.06, and for transverse flow to be about 8. A simple model is derived to illustrate the role of capillary flow along fiber reinforcements during wetting. While capillary flow is insignificant with high injection rates, it is significant at low injection rates. The model indicates that for a specified fiber volume fraction in the fiber bundle, there exists a unique injection speed in which the bulk fluid flow front matches the capillary flow front inside the bundle. Injection at that speed is usually too slow to be practical, but it would substantially reduce the void content in fiber bundles after impregnation. At high injection rates, the model indicates the possible trapping of air inside fiber tows due to the capillary flow lagging behind the bulk flow.