Axial flows in generalized ducts are analyzed fur viscoplastic materials behaving as Bingham plastics with a yield stress, A constitutive equation proposed by Papanastasiou is used, which applies everywhere in the flow field in both yielded and practically unyielded regions, Numerical simulations are presented in several two-dimensional cross-sectional geometries, such as square and rectangular ducts (straight and concave), and eccentric annular conduits, for different flow rate and pressure drop ranges. The extent and shape of yielded/unyielded regions are shown as the dimensionless yield stress or Bingham number increases. Master curves are given for the dimensionless flow rate vs dimensionless pressure drop or vs Bingham number for quick engineering calculations useful in practical applications of materials processing.