Viscoplastic fluids have wide industrial applications. There have been a lot of research works published on plastic flow of the Bingham type, but comparatively few have been devoted to flow of nonlinear viscoplastic fluids in non-circular ducts. The duct flow of nonlinear viscoplastic fluids is analyzed through the finite-element method. The location of the yield surface is determined by the regularization technique. Two kinds of duct, namely the eccentric annulus and square duct, are investigated. These flows are seen to consist of mobile plug zones in the duct center with stagnant plugs 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.