Tissue engineering aims to produce artificial organs and tissues for transplant treatments, in which cultivating cells on scaffolds in bioreactors is of critical importance. To control the cultivating process, the knowledge of the fluid flow inside and around a scaffold in the bioreactor is essential. However, due to the complicated microstructure of a scaffold, it is difficult, or even impossible, to gain such knowledge experimentally. In contrast, numerical methods employing computational fluid dynamics (CFD) have proven promising to alleviate the problem. In this research the fluid flow in perfusion bioreactors is studied with numerical methods. The emphasis is on investigating the effect of the controllable parameters in both the scaffold fabrication (i.e., the diameter of scaffold strand and the distance between two strands) and cell culture process (i.e., the flow rate) on the distribution of shear stress within the scaffold in a perfusion bioreactor. The knowledge obtained in this study will allow for improved control strategies in scaffold fabrication and cell culturing experiments.