The flow of solid particles suspended in a liquid medium have great importance in several industry segments representing an economical way to transport large quantities of solid materials. One of the applications includes the flow during directional well drilling. During the process sediments are generated from the formation cutting, which are removed through the wellbore cleaning. During the cleaning, step near the horizontal section of the well, these sediments tend to separate from the suspension by the action of gravity, forming a stationary bed in the bottom of the annular. This stationary bed can cause problems, such as reducing the penetration rate, premature wear of the drill bit, trapping column, fracturing of the formation and high torque. The complete understanding of the flow of solid particles suspension becomes relevant to the improvement of these processes. In this sense, the main goal of this work is to analyze the flow of solid particle suspensions between two parallel plates to investigate the formation of a stationary bed in the bottom of the channel and to determine the effect of different particle migration mechanisms in this process. The mathematical formulation includes the equations of mass (continuity equation) and momentum conservation. The Diffusive Flux Model proposed by Phillips et al. (1992) was used to describe the particle transport in the flow. The partial differential equations, which describe the flow of solid particles suspension, are solved by the Galerkin/Finite Element Method (GFEM) and the non-linear system is solved using Newton s Method. The results show how the distribution of solid particles varies with the problem parameters and determines the conditions for the formation of a stationary bed.