Viscoplastic fluids are well known in industry. There is a huge literature on plastic flow of the Bingham type, but comparatively little has been published on the flow of generalized viscoplastic fluids in non-circular ducts. The present study analyzes the duct flow of generalized viscoplastic fluids using a finite-element method. The problem of tracking the yield surface is solved by the regularization technique whose existence theorem has been established through the theory of variational inequalities. Flows in eccentric annuli and a square duct are investigated. Mobile plug zones exist in the duct center. Stagnant plugs exist at the narrow side in eccentric annuli at large eccentricity or large Bingham number, and near the apex of corners in a square duct. It is shown that the sizes and the contours of the plug zones are mainly determined by the force balance between transverse shearing and yield stress. In addition these zones are almost identical for various plastic models considered here despite their different shear-thinning behaviors.