A numerical procedure has been developed for the design of duct elbows that exhibit minimum pressure loss. A two-dimensional potential flow modeling method is used to determine the ideal static pressure distribution for a given elbow geometry. A turbulent boundary layer separation criterion is then used to determine whether the ideal distribution can be obtained. Those elbow designs for which flow does not separate are shown to produce minimum pressure loss. The procedure is also shown to be effective in the design of turning vanes. The design method is confirmed by experiments with a 90 degree elbow within a square duct.