Accurate determinations of excess pressure losses at the entry and exit of capillary flows are essential for rheological characterization of fluids by capillary viscometry. A modification of Bagley’s end correction method is presented which accounts for the effects of slight variations in the diameters of the tubes of varying length used in the evaluations. The method was applied to capillary flows of dilute aqueous Polyox solutions using the three homologues WSR 301, Coagulant and FRA of Polyox. The excess pressure losses were found to increase with increase in the apparent shear rate, polymer concentration and tube diameter.