Inaccurate prediction of the required pressures can lead to a number of costly drilling problems. In this study, the hydrodynamics of mud-cuttings were numerically studied using the Mixture Model. To this end, an in-house code was developed to calculate the velocity and pressure fields. The mud velocity profile using of Herschel–Bulkley model and solid phase volume fraction were locally calculated; moreover, pressure drop through the annulus was taken into account. The effects of velocity, mud properties, and solid phase volume fraction on pressure drop were discussed and a new correlation was proposed for calculating friction factor based on corresponding parameters.