Problem statement: Oil well cleaning is the ability of a drilling fluid to suspend and transport drilled cuttings from the down hole (bit face) to the surface. The cleaning performance was affected by many factors such as fluid viscosity, annular flow velocity, angle of inclination and drill cuttings size and shape and. Approach: Navier-Stoke equations, the continuity equation and the power law of non-Newtonian viscosity model were adopted to establish the mathematical model of the cutting transport process in the annulus of the well. The constants of the power law model were evaluated experimentally for three different mud types. The CFD simulation to solve the governing equations was carried out by using FLUENT commercial code. The specifications of the particles, the pumping head and feeding conditions were obtained from a drilling site in Sudan. Results: Simulation of the mud flow in the annulus had shown that in spite of the laminar nature of the flow, the velocity profile was flattening over wide area of the annulus. Such condition was referred to as fog flow and was preferable to produce uniform drag distribution to lift the particles without rotation during the transportation process. The analysis had been conducted for various mud charging rates ranging from 600-900 GPM, in 30° diverted orientation well. The investigation of cuttings size was conducted for 2.54, 4.45 and 7 mm. Also, the effect of the cuttings shape with 1, 0.9 and 0.85 was investigated and it was found that higher sphereicity have better cleaning efficiency. Conclusion: The analyses revealed that for 30° diverted orientation; the effective cleaning performance was achieved when the drilling mud charging was higher than 800 GPM for all types of tested cuttings. The simulation results revealed that there was a significant effect of the cuttings size on the cuttings transport. Fine particles are the easiest to clean out. © 2010 Science Publications.