In this study, a mathematical model has been developed for the submerged membrane bioreactor (SMBR). Polyvinyl alcohol (PVA) Modified Non-woven model is immerged in MBR to be used for synthetic wastewater treatment. The results show that membrane fouling resistance is mostly cake resistance occurring during filtration. Based on the concept of specific fouling resistance and Darcy law that describes the relationship between flux and resistance during filtration driven by pressure, a module is established to explain the relationship between specific fouling resistance and time during filtration controlled by cake resistance in SMBR. The decline trend of flux can be predicted by the model. The model is used to predict the decline trend of flux during pharmaceutical wastewater treatment. Compared with experimental data, the relative error is less than 10% at t>b, the relative error is less than 5% at t>2b. It shows that the model can predict the decline trend of flux during stable operation of SMBR. But the relative error is bigger during unstable operation at initial stage (t<b). The model developed in this study would provide a useful tool in optimizing operation conditions as well as design parameters for a SMBR system.