The growth of tumors and their response to treatment are determined by delivery of diffusible substances to cancer cells and hence by their blood supply. Relative to most normal tissues, tumor blood flow is highly heterogeneous. Several hypotheses have been postulated to explain this anomalous behavior of tumor microcirculation, but the underlying mechanisms for these heterogeneities are not fully understood. In this study we consider a potential source of nonuniformity in the blood flow: the enhanced fluid exchange between the vascular and interstitial space mediated by the high leakiness of tumor vessels which could lead to a coupling between vascular, transvascular, and interstitial fluid flow. A simple network model is presented to describe the basic features of flow through a network of permeable and compliant vessels embedded in an isotropic porous medium. Two vascular geometries are considered: a regular mesh of identical vessels and a pair of countercurrent vessels of equal diameter. In each case, the flow through each vessel of the network is described by Poiseuille's law; the transmural flow between the vessels and the external porous medium is governed by Starling's law; the fluid movement through the porous medium is described by Darcy's law; and the vessel wall is assumed to be elastic. Our results show that the behavior of microcirculation may be strongly modified as a result of vascular compliance and enhanced vascular leakiness of tumor vessels. We found not only that the vascular pressure generates the well-known, high central interstitial fluid pressure, but also that the elevated interstitial pressure in turn alters the vascular pressure distribution. These changes in vascular pressure distribution result in a modification of the blood flow pattern. As the leakiness and compliance of the vessels increase, the blood is diverted away from the center of the tumor to a more peripheral path. The clinical significance of these results is that drug delivery for chemotherapy and oxygenation needed for radiotherapy may well be hampered in the central region of the tumor, despite the presence of highly permeable vessels in these regions.