This article examines the concentric and eccentric annular flow of non-Newtonian fluids. A new effective diameter definition that accounts for flow geometry and fluid rheology is presented for pressure loss prediction. Satisfactory agreements were obtained between this new effective diameter definition in combination with laminar Fanning friction factor correlations and extensive flow data in the literature. In addition, an explicit friction factor correlation as a function of the generalized Reynolds number, diameter ratio, and relative roughness is presented for a fully eccentric annular drag-reducing turbulent flow. A good agreement was obtained between this correlation and the gathered flow data. The correlations reported provide an effective means of determining friction pressures of non-Newtonian fluids in eccentric annuli.