Drop and bubble motion are important in many scientific problems including the movement of bubbles created during the boiling process in boilers, water and oil flow in pipes, oil recovery in porous media and mixed mineral particles in water. Migration of deformable drops in different flows has been the subject of many empirical and theoretical researches including shear flow which has been studied in recent years in order to investigate the effect of different parameters on the way drop migrate, and has been studied in the present thesis as well. Generally in transfer processes such as mass transfer process the droplet distribution in the width of the channel is of importance. In this project the traverse movement of the droplets and distribution of droplets with different sizes across the width of the channel is discussed. In the present study, flow with two groups of droplets with different sizes with the same diameter ratio are considered. In order to examine the effect of initial droplets arrangement on the final results, two different initial arrangements have been used. Two different size ratios is used to evaluate the effect on the final results. The results are obtained from numerical solution of the Navier- Stoks equations with no simplification and with consideration of surface tension force. The numerical method used here is a finite different front tracking method. In this investigation effect of dimension less parameters such as the Reynolds number and the size ratio is studied on segregation of droplets with different sizes in the flow. In all of the simulations a free surface boundary condition is applied at the top. Also for two boundries perpendicular to the flow the periodic boundary condition is considered. Results of the simulations show that by increasing Reynolds number, droplet segregation is enhanced. Also at large size ratio, drops with larger size reach an equilibrium position which is farther from the channel floor. In other words the drop density distribution shows that larger drops move to upper half of channel, whereas smaller drops move to lower half of channel‌‌‌‌‌‌‌‌‌‌‌. If the size ratio increases the total number of drops in the channel will also increase. This will reduce the fluctuation energy of the flow. The fluctuation energy also increases when the Reynolds number is raised. As it has been expected the initial droplet arrangement does not have a considerable effect on the results. Keywords: Drops,Particle Size Segregation, Size Ratio,Density Distribution