The augmented Lagrangian method is applied to the steady flow problems of Bingham, Casson and Herschel-Bulkley fluids in pipes of circular and square cross-sections. The plug flow velocity, the flow rate, the flow pattern, the velocity profile, the locations of yielded/unyielded surfaces, the stopping criteria and the friction factor are presented and compared with one another. The numerical strategy based on variational inequalities is shown to be realised easily and applicable extensively. (c) 2005 Elsevier B.V. All rights reserved.