The flow of suspensions through channels and tubes has been the subject of many investigations. The flow of slurries, the recovery of oil, the traort of oil and water through pipelines, and food and material processing are typical application of these flows. Since the distribution of drops through of the channel determines the flow rate, lateral migration of drops and their final equilibrium position is of particular interest. Suspensions of two-dimensional drops in simple shear flow are studied at nonzero Reynolds numbers by numerical simulations. The flow is studied as a function of the Reynolds number, the Capillary number and the drop sizes. Results are obtained using a finite diffrence/front tracking method in a periodic domain. Suspension of drops at a moderate areal fraction ( ?=0.44) is studied by simulations of 36,144 and 288 drops. It is found that the effective viscosity decreases with Capillary number and the normal stress difference increases. The results for the normal stress difference show oscillations around a mean value at small Reynolds numbers, and it slightly increases as the Reynolds number is raised. It is also found that similar to flows of granular materials, suspension of drops at finite Reynolds numbers shows the same trend for the density and fluctuation energy distribution across the channel. Similar to the motion of a single drop, drops migrate away from the walls. It is found that the size of the clusters decreases with Capillary number and Reynolds number. Other achievements are that an decrease in the size of the drops leads to a reduction in the size of the clusters, and that for highly deformable drops almost no cluster forms. These phenomena is due to the more freedom of the drops while displacement. It was observed that the diagrams of the effective viscosity and normal stress difference pertained to the small-sized drops include less oscillations compared with the large-sized drops, which can be related to the reduction in the size of the clusters. Examining the diagrams of the density, it was inferred that the transverse immigration of the drops toward the center of the channel increases with an increase in the capillary number. Also, the diagrams associated with the fluctuation energy suggest that this quantity increases with an increase in the value of the Reynolds number. The reason must be sought on one hand in the decrease in the size of the clusters, and on the other hand in the increase in the number of collisions. Furthermore, it was reported that while the deformability of the drops enhances, the reduction in the number of collision between the drops causes a decrease in the value of the fluctuation energy. Also, the fluctuation energy of the flow is found to firstly approach higher levels with an increase in the number of the drops, and then reach a limit value. This may be attributed to the increase in the number of the collisions Keywords : Two-phase flow, Front Tracking, Drop, Shear flow