The purpose of this study is to improve the design of a bioreactor for growing bone and other three-dimensional tissues using a computational fluid dynamics (CFD) software to simulate flow through a porous scaffold, and to recommend design changes based on the results. Basic requirements for CFD modeling were that the flow in the reactor should be laminar and any flow stagnation should be avoided in order to support cellular growth within the scaffold. We simulated three different designs with different permeability values of the scaffold and tissue. Model simulation addressed flow patterns in combination with pressure distribution within the bioreactor. Pressure build-up and turbulent flow within the reactor was solved by introduction of an integrated bypass system for pressure release. The use of CFD afforded direct feedback to optimize the bioreactor design.