Normal force is measured which is generated in the flow between two rollers, one rotating and the other fixed. Aqueous glycerin solutions are used as Newtonian fluids, and dilute solutions of polyethylene oxide (PEO) and polyacrylamide (Separan) are used as viscoelastic fluids at concentrations of 50–1000 ppm in weight. The force measured for viscoelastic fluids is larger than that for Newtonian fluids. The normal force for Newtonian fluids is evaluated by applying the Cameron’s theory with the Reynolds equation and the half Sommerfeld condition. It is found that the calculated force agrees well with the experimental result. The normal force for viscoelastic fluids is predicted using the same assumptions as for Newtonian fluids except the constitutive equation of Coleman–Noll. The predicted expression is in good agreement with the present experimental result for dilute PEO solutions but roughly agree with the data for nondilute PEO and Separan solutions.