The availability of large numbers of units of artificial arteries would offer significant benefits to the clinical management of bypass surgery. Tissue engineering offers the potential of providing vessels that can mimic the morphology, function, and physiological environment of native vessels. Ideally this would involve culturing stem cells in vitro within a biodegradable tubular scaffold so as to construct tissue for implantation. Essential to establishing a robust process for the production of tissue-engineered arteries is the understanding of the impact of changes in the operating conditions and bioreactor design on the construct formation. In this article, models of transport phenomena were developed to predict the critical flow rates and mass transfer requirements of a prototype bioreactor for the formation of tissue-engineered arteries. The impact of the cell concentration, tube geometry, oxygen effective diffusivity in alginate, substrate and metabolite concentration levels, feed rate, and recycle rate on tire design of the bioreactor was visualized using windows of operation and contour plots. The result of this analysis determined the best configuration of the bioreactor that meets the cellular transport requirements as well as being reliable in performance while seeking to reduce the amount of nutrients to be used. (C) 2009 American Institute of Chemical Engineers Biotechnol. Prog., 25: 842-853, 2009