Renal failure or kidney failure is a medical condition when the kidneys fail to filter toxins and waste products from the blood. Most of the time, problems encountered in kidney malfunction include abnormal fluid levels in the body, increased acid levels and abnormal levels of Urea, Glucose, Endothelin, β2-Microglobulin, Complement Factor D. In medicine, dialysis is a method that is used to remove waste products from blood when the kidneys are in a state of renal failure. Parameters characterizing the structure of dialyzers are very important because they decide overall clearance of toxin molecules and at the same time should allow retaining useful molecules in the blood. It is however not clear how the changes of dialyzer parameters will affect the clearance. This can be found out by doing simulation of a dialysis process. In this thesis, a numerical model was developed to simulate the process that goes on inside a dialyzer to determine which parameters are important for getting better clearance of toxin molecules and how the changes of those parameters can improve the performance of dialysis. In order to do that, a model of dialyzer membrane with details of the porosity is necessary. The dialyzer membrane that was considered in this research was Polyflux 210H. Here the cross sectional images of Polyflux 210H dialyzer membrane were taken by FESEM (Field Emission Scanning Electron Microscope) to obtain the porosity values of different layers. Using these porosity values, a multilayered membrane model was developed in Finite Element Software- COMSOL Multiphysics 4.3. Then a blood flow containing - Urea, Glucose, Endothelin, β2-Microglobulin, Complement Factor D and Albumin was introduced. For a certain blood flow rate the toxins diffuse through the membrane and on the other side of the membrane a dialysate flow was introduced to remove the toxins. Two different definitions of effective diffusivity were considered for the phenomenon of the diffusion of the molecules in the membrane. Between the two, the better definition was found out by comparing the results with experimental data of the manufacturer of Polyflux 210H. Then for the chosen definition, further analysis was done and the results were compared with another set of experimental data to validate the model. Then different parameters - magnitude and direction of both blood and dialysate flow, length and diameter of the fiber, pore sizes were changed to simulate how these changes affect toxin clearance and the removal of useful molecules. The results suggest some very interesting points to achieve better dialysis performance. First of all, the clearance rate of both Urea and Glucose increase rapidly with the increasing blood flow rate. When a maximum allowable blood flow rate is attained, increasing the dialysate flow rate can ensure better clearance rate for Urea and Glucose. In both the cases of increasing radius or length of the dialyzer fiber, the clearance rate of Glucose increases more rapidly than the clearance rate of Urea. For Endothelin and β2-Microglobulin the clearance rate increases twice compared to the initial condition. Meanwhile, the clearance rate of Albumin does not change that much. Also increasing the pore diameter up to 20 nm (but not more than that) can ensure higher clearance rate of Urea and Glucose, moderate clearance rate of middle molecules and minimum loss of Albumin.