In the oil industry, there are many situations where fluid flow in annular spaces ta kes place. During the oil well rotary drilling for instance, the drill bit oscillations change the well cross-section from an expected circular to an elliptic shape. In these cases, the drilling fluid flow through the annular space that is molded between the drill string and the rock formation is a matter of concern s o that the correct eva luation of pressure drop a nd shear stress distribution along the borehole is qu ite important for an appropriate well design. Despite its importance, studies related to non-Newtonian fluid flow through eccentric or even concentric elliptical annuli are not reported in the open literature. Therefore this paper presents an analytical friction factor correlation for viscoplastic fluid flow through two types of elliptical cross-sectional ducts: a concentric elliptical annulus and an eccentric one. The solution is based on the slot flow model of variable height that is validated comparing the results with the literature and with numerical results obtaine d from computational fluid dynamics. Very good agreement for the eccentric annular pipe was obtained from the comparison between the current analytical results and the numerical solutions from the literature. A promising application of the present analytical solution for the eccentric elliptical annular duct flow was found when comparing the results with computational fluid dynamics ones.