A computational fluid dynamics (CFD) model is developed to simulate the flow and delivery of oxygen and other substances in a capillary network. A three-dimensional capillary network has been constructed to replicate the one studied by Secomb et al. (2000), and the computational framework features a non-Newtonian viscosity model of blood and the oxygen transport model including in-stream oxygen-hemoglobin dissociation and wall flux due to tissue absorption, as well as an ability to study delivery of drugs and other materials in the capillary streams. The model is first run to compute the volumetric flow rates from the velocity profiles in the segments and compared with Secomb’s work with good agreement. Effects of abnormal pressure and stenosis conditions, as well as those arising from different capillary configurations, on the flow and oxygen delivery are investigated, along with a brief look at the unsteady effects and drug dispersion in the capillary network. The current approach allows for inclusion of oxygen and other material transports, including drugs, nutrients, or contaminants based on the flow simulations. Also, three-dimensional models of complex circulatory systems ranging in scale from macro- to microvascular vessels, in principle, can be constructed and analyzed in detail using the current method.