A few additional data from our previous experi-ments were plotted to emphasize the shear-thickeningbehavior of deoxy sickle erythrocyte(SS)suspension.A con-stitutive equation(named as FX equation)was developed andapplied to a cylindrical pipe flow of a shear-thickening fluid.A blunt velocity profile and its volume flow rate were cal-culated.The flow was non-viscous(potential)in the centralpart of the pipe(i.e.the central core or the central plug-flow),and became more and more viscous towards the wall of thepipe after a specific radial distance,which was determinedby a critical shear rate of(?)F(named as Fung’s shear rate).Furthermore,combining the FX equation with the originalCasson’s equation,the author obtained a modified Casson’sequation by introducing(?)F. A few additional data from previously previous-ments were plotted to emphasize the shear-thickening behavior of deoxy sickle erythrocyte (SS) suspension. A con-stitutive equation (named as FX equation) was developed andapplied to a cylindrical pipe flow of a shear- thickening fluid. A blunt velocity profile and its volume flow rate were cal-culated. flow was non-viscous (potential) in the central part of the pipe (iethe central core or the central plug-flow), and more more and more viscous towards the wall of the pipe after a specific radial distance, which was determined by a critical shear rate of (?) F (named as Fung’s shear rate) .Furthermore, combining the FX equation with the originalCasson’s equation, the author obtained a modified Casson ’ sequation by introducing (?) F.