This paper concerns an experimental and computational study of the laminar flow developed by a pseudoplastic fluid through a partially-obstructed annulus, considering the effects of eccentricity and inner cylinder rotation. For the eccentric cases the eccentric rotation of the inner tube is applied, which is a novelty in the literature. Pressure drop experimental data are reported for flows of 3 and 9m(3)/h of a 1 mg/g xanthan gum aqueous solution through a concentric and a 46% eccentric annulus with partial obstruction of 6mm, for cases with and without rotation of the inner cylinder (0 and 400 rpm). Numerical simulations were performed using computational fluid dynamics (CFD) techniques which allowed for reporting of axial velocity profiles, apparent viscosity distribution, and pressure drops for a range of eccentricity values (0, 23, and 46 %) and obstruction heights (0, 6, and 12 mm), which were systematically compared for cases with and without rotation of the inner tube (0 and 400 rpm). Comparisons between numerical calculations and the flow data indicated, in general, very close agreement. Eccentric rotation of the inner cylinder presented a distortion effect on the axial velocity and apparent viscosity profiles for the high eccentricity case (46 %) with high obstruction (12 mm), where two maxima regions were observed, one of them near the inner cylinder.