A mathematical model has been developed which describes the fluid exchange from a capillary network of realistic topology, and calculates the spatial distribution of extravascular pressure. In this model, the capillaries are represented by a superposition of sources and sinks, resulting from a D'Arcy's Law description of flow in tissue of uniform fluid conductivity. The combination of this representation and Starling's Hypothesis, which relates the forces influencing transmural fluid exchange, yields an integral equation of the second kind which is solved numerically for the source strength distribution. Two important features of this approach are that: (i) it allows for interaction between the local tissue pressure field and fluid exchange (the model is called, therefore, the tissue pressure interaction model); and (ii) complex network morphologies are easily modeled. In single capillaries, this interaction, which decreases the predicted fluid exchange, increases with the magnitude of the ratio of capillary wall to extravascular fluid conductivities. For multiple capillaries, in addition to the "self" interaction of a capillary with the local extravascular pressure field, there is the possibility of interaction between capillaries ("capillary-capillary" interaction). The ratio of conductivities, and the additional factors of intercapillary distance and the number of capillaries, also affect interaction in capillary networks. Although interaction is only a weak function of intercapillary distance, it depends strongly on the number of capillaries. The major result from this work is that for the entire physiological range of conductivity ratios, interaction cannot be neglected in predicting fluid exchange. Although tissue pressure interaction affects the magnitude of fluid exchange, it does not greatly alter the pattern of extravascular flow. Therefore, previous models which neglected interaction are not invalidated by the present findings. The effect of interaction on planar capillary networks within a semi-infinite tissue space was also investigated. Flow boundary conditions were imposed at opposed planar boundaries, parallel with the capillary network. Interaction was found to decrease with decreasing distance between the boundary and plane of the capillaries. It still exerted a large effect, however, for distances greater than one-fourth the reference capillary length.