Steady, two-dimensional flows of Bingham fluids are analyzed by means of a modified constitutive relation that applies everywhere in the flow field, in both yielded and practically unyielded regions. The conservation equations and the constitutive relation are solved simultaneously by Galerkin finite element and Newton iteration. This combination eliminates the necessity for tracking yield surfaces in the flow field. The analysis is applied to a one-dimensional channel flow, a two-dimensional boundary layer flow, and a two-dimensional extrusion flow. The finite element predictions compare well with available analytic solutions for limiting cases.