The steady flow of an incompressible material of the Bingham viscoplastic type along a rectangular duct is calculated. This flow has importance in a number of geophysical problems. A numerical solution to the problem is found using finite differencing of the partial differential equation governing the fluid motion. The flow is seen to consist of a plug in the center of the duct with dead regions of “no-flow’’ at the corners, due to the rectangular cross section. The variation of this flow pattern as a function of two nondimensional parameters, the yield stress and the aspect ratio, is investigated.