This paper expands the current model. for laminar displacement of one Power-law fluid by another in concentric horizontal annuli (Nguyen and Rahman, 2000), to take into account the effect of eccentricity. A calculation procedure is also presented. which can be used for computer modelling of laminar displacement process in eccentric horizontal annuli, Simulated results clearly demonstrate the detrimental effect of eccentricity on the displacement process, and suggest that the How velocity in the narrow part of an eccentric annulus should be one of the major design considerations for an effective horizontal annular displacement.