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This paper numerically investigates the influence of Hall current on the steady flows of an Oldroyd 6‐constant fluid between concentric cylinders. The flow analysis has been performed by employing finite element method. Two flow problems are considered. These problems have been recently solved by Rana  et al.  ( Chaos, Solitons and Fractals , in press). Here the main equation governing the flow problems in ( Chaos, Solitons and Fractals , in press) is corrected first and then used in the simulation. Finally, the interesting observations are obtained by plotting graphs. Copyright © 2008 John Wiley & Sons, Ltd.