A fascinating and largely unsolved problem in tribology concerns the effect of visco-elasticity on lubrication flow characteristics. The paper has re-addressed this problem by using a perturbation method. The impact of the paper is that we theoretically provide an asymptotic solution based on the flow between two narrow surfaces with a convected Maxwell model and show that the viscoelasticity does indeed produce a beneficial effect on lubrication performance characteristics. We also prove that the solution given by Prof. Tichy, who is the chief editor of the Journal of Tribology, appears erroneous.