A bioartificial pancreas, consisting of immobilized islets encapsulated within hollow fibers, is investigated as an alternative treatment for insulin-dependent diabetes. A mathematical model is developed to determine whether this configuration of the bioartificial pancreas can yield an insulin response to a glucose challenge with the appropriate dynamics in diabetic humans. The model consists of the 2-D mass-conservation equations for glucose and insulin within the hollow fiber and capillaries. The equations contain terms for insulin-production kinetics by porcine islets and glucose-consumption kinetics. The boundary conditions account for transport resistances of the fiber membrane, the tissue surrounding the implant, and a thin film within the capillaries. The equations are coupled to a pharmacokinetic model of the circulatory system. The calculations show that an optimized design with this configuration will be feasible for human use and requires a total volume of 4.6 mL to reach the target insulin concentration in the bloodstream following a glucose challenge. The parameters and processes controlling the system performance are discussed.