In the design of perfusion bioreactor system for tissue engineering, design parameters including fluid dynamics and mass transport as well as scaffolds should be optimized to maximize cell growth. Critical elements in bioreactor systems based on cells and scaffolds include cell seeding, the nutrient and gas supply to cells, and mechanical stimuli. In particular, perfusion flow systems have been shown to enhance cell growth, differentiation, and tissue formation as well as provide for the appropriate and necessary mass transfer of nutrients, gases, metabolites, and regulatory molecules. In this paper, we reviewed the biomechanical models in relation with fluid dynamics, mass transport, and shear stress with scaffolds. Therefore, obtaining a proper oxygen supply, high cell density, and an uniform cell distribution in a three-dimensional growth support are important. Both experiments and quantitative mathematical models of cell culture in perfusion bioreactors; are needed to better understand physical, mechanical, and biochemical conditions and for the design of a suitable bioreactor system the mathematical describes the oxygen mass transfer and cell density within a three-dimensional scaffold. This review focuses on biomechanical models in relation with fluid dynamics, mass transport, and shear stress to cells cultured, and cell growth in perfusion bioreactors for tissue engineering.