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It is presented a general procedure to calculate the modification of the basic equation for hydrodynamic lubrication brought about by the use of polymeric fluids with shear depending viscosity. The procedure is based on the generalized newtonian fluid model and allows to treat all type of flows. For a given function between viscosity and shear stress the results show that the influence of the non-Newtonian behavior is completely characterized by one dimensionless number, namely where U is the relative sliding velocity, h* is the characteristic film thickness and τ* a characteristic time of the lubricant. The use of the procedure is exemplified applying it to determine the relation between hydrodynamic lubrication and average molecular weight, molar mass distribution and concentration of the polymer component and the viscosity of the solvent or polymerfree oil. Some practical aspects of this relation are discussed.