The paper presents an interesting result in non-Newtonian effects on lubricant thin film flow using an asymptotic expansion technique. The result shows that the viscoelasticity does indeed produce a beneficial effect on lubrication performance, which is consistent with experimental observations. The impact for this paper is to provide a theoretical treatment for the analysis of the effects of non-Newtonian fluids on the thin film flow, such as lubricants in journal bearing systems.