Abstract: By using complex function theory and Finite Element Method,creeping drag laminar flows of Newtonian and Non-Newtonian Fluids between plates are numerically studied,and the influence from Reynolds Number,shear-thinning coefficient and blockage-passage ratio on the emergence and evolvement of vortex is analyzed.Researches indicate that with some qualifications,the increase of Reynolds Number also would bring out vortex and enlarge the areas vortex affects,but this influence is limited.The reason why Reynolds Number is not the key factor to vortex is the great velocity gradient inside the flow.With different profiles of substrate plate,the influence from Reynolds number on vortex is similar.While for the Non-Newtonian Fluids,shear-shinning coefficient puts little impact on the flow configuration,but its augment heightens the position where flow separation occurs and boost up the range and intensity of vortex,which makes the flow field further unsteady.As the average plate-distance increases,the absolute value of critical waviness also enhances,while the blockage-passage is on the contrary,which shows that critical blockage-passage trends to decrease with the augment of waviness.