A proposed viscosity model for Yield Power-Law fluid by Souza Mendes and Dutra (SMD), devoid of discontinuities at vanishing shear rate, is adopted in a 3D CFD simulation study. Radial distributions of axial, tangential, and coupled components of velocities are measured along concentric and eccentric narrow annuli. The flow is assumed to be fully-developed, laminar, and steady state. Several parameters such as diameter ratios, eccentricities, and inner pipe angular speeds were varied to analyze their influence on the flow distributions and annular pressure losses. The simulated results of radial distributions of axial and tangential velocities show good agreement with experimental data and analytic solutions from previous studies. Annular flow instabilities in the form of Taylor vortices in the flow fields are briefly discussed. This study shows how reliable CFD simulations can replicate the actual, yet complex, oil and gas drilling operations.