Solutions are obtained for steady‐state low Reynolds number flow of viscoplastic materials in systems with recirculating eddies using the finite‐element method. The reattachment length and eddy intensity in planar and axisymmetric abrupt expansions are correlated with Reynolds number and dimensionless yield stress for Bingham and Casson materials. Flow in a stenosis is examined using Newtonian and Casson constitutive relationships. The separation zones in a 180 degree planar bifurcation with straight and bent inlets are compared for Bingham and Newtonian fluids. The results show that the size and strength of recirculation is reduced for viscoplastic materials.