Abstract: Fluid shear stress (FSS) induced in the microfluidic bioreactor under the driven loads of applied external physical fields (Fluid pressure gradient or Electric filed), which make the cells regulate its genes expression and promote differentiation and growth, so does in the natural tissue microtubule system. It is difficult to experimental quantifications the fluid flowing behavior in the cell culture chamber. The theoretical modeling is thought to be an effective way. In this paper, a theoretical model for microfluidic flow in the rectangle cell culture chamber is developed to link the applied external physical fields (pressure gradient and electrical field) to intraluminal fluid velocity (FV), FSS and fluid flow rate (FFR). The results predict the model solutions are nearly match the others experiment results. Specifically, the solutions under pressure-electricity synergic driven are the superposition of the driven solutions of each pressure gradient and the electric field. FSS, FV and FFR amplitudes in chamber are proportional to the amplitudes of applied external physical fields, but decrease and change little as the frequencies of pressure gradient and electric field grows, respectively. The higher chamber height is, the larger FSS and FFR amplitudes generalized in the pressure gradient driven model, while not obvious change in the electric field driven model. Besides, the results are not influenced when the culture medium temperature varies at the physiological level. At the generalized cell response level, electric field driven model can provides the larger FSS amplitude, while the pressure driven flow model is good at inducing the larger FFR amplitude. The combined pressure-electricity synergic driven model can be used as the theoretical basis to design the experimental cell microfluidic bioreactor system, meanwhile, provides the references to research the mechanism of cell growth and differentiation under the stimulus of （shear）stress and electricity.