The paper concerns numerical study of fully developed laminar flow of a Newtonian water and non-Newtonian fluids, 0.2% aqueous of sodium carboxymethyl cellulose(CMC) solution in eccentric annuli with combined bulk axial flow and inner cylinder rotation. Pressure losses and skin friction coefficients have been measured when the inner cylinder rotates at the speed of 0～200 rpm. A numerical analysis considered mainly the effects of annular eccentricity and inner cylinder rotation. The present analysis has demonstrated the importance of the drill pipe rotation and eccentricity. In eccentricity of 0.7 of a Newtonian water, the flow field is recirculation dominated and unexpected behavior is observed. it generates a strong rotation directed layer, that two opposing effects act to create two local peaks of the axial velocity. The influences of rotation, radius ratio and working fluid on the annular flow field are investigated.