A cuttings bed formed on the lower side of the wellbore is the most common drilling problem confronted when horizontal or highly deviated wells are drilled. The phenomenon is undesirable and has a detrimental effect on wellbore hydraulics and drilling performance. To achieve an efficient drilling operation, hydraulics optimization should be implemented by precisely predicting annular pressure loss and other hydraulic parameters.The accumulation of cuttings at the lower side of horizontal or highly inclined wellbores, combined with wellbore eccentricity and fluid rheological properties, create a complex behavior of pressure loss. In this study, a numerical approach is used to investigate the influence of the aforementioned factors. A numerical solution is performed for laminar flow of non-Newtonian fluids. A non-orthogonal, boundary-fitted curvilinear coordinate is developed, which is based on elliptic partial differential equations (PDE) to accommodate annular flow geometry with arbitrary cross-sections. Finite difference numerical schemes adapted to the coordinates is then used to analyze the problem. The numerical model determines the effect of hydraulic parameters of fluid flow thorough an irregularly shaped annulus and considers the following factors: flow rate, fluid rheological parameters, annular geometry and bed appearance. Numerical predictions from the model are verified against existing models and experimental data in literature; and good agreements are obtained. The developed numerical model can be combined with a 1-D solids transport model for designing oil and gas well drilling operations.