Among the costs considered on an oil field exploration, the drilling process related ones constitute a significant share. Consequently, the focus on the removal of cuttings generated by the drilling process, or the hole cleaning operation, is essential. This operation remains a critical issue in the drilling of high inclination-wells, since the cuttings tend to deposit themselves due to gravity´s action, forming a bed in the annular space formed between the drill string and the casing. When this bed takes a sizable fraction of the annular space, it becomes responsible for many problems that appear on the drilling stage, such as premature bit´s exhaustion, low rates of penetration, formation fracture, excessive torque and drag on the drillstring, stuck pipe, fluid flow interruption, etc. If this situation is not treated properly, it may cause the loss of the well. This present thesis proposes a model for multiphase flow in the wellbore drilling, capable of evaluating the formation of the cuttings´ bed and to predict oscillations of pressures in annulus due to the flow. A two-layer model is adopted, where the annular space is divided in two regions: bed and suspension. The bed (Region 1) is formed by the cuttings, which were deposited due to the action of gravitational force, while the suspension (Region 2) is the portion of the annular above the deposited bed, formed by the drilling fluid and cuttings. The constitutive equations of the aforementioned model are given by the equations of mass conservation for solids and liquids and the momentum conservation equations for the bed and the suspension. The finite volumes method was used to turn the differentials equations into discrete ones, while the Newton´s method was applied for the solution of the nonlinear system of equations. The solution is given through the following variables: bed height, solid velocity and fluid velocity both in bed and suspension, annular pressure and solid concentration in the annular. Examples of application of the methodology are presented, showing the behavior of the involved variables through time. The examples show the efficacy of the methodology to simulate drilling operations, in special hole cleaning ones.