The lateral migration of deformable particles in shear flows has been the subject of many investigations. The lateral migration of immersed objects in carrier fluids becomes very important in traort processes, where mass, momentum and energy are exchanged. Removal of the vapor bubbles from the walls of pipes enhances the heat and mass transfer rates. The lateral migration of a buoyant drop in simple shear flow is studied numerically in two dimensions. For a slightly buoyant drop, the drop migrates to an equilibrium position which is close to the walls depending on whether the drop leads or lags the flow. If the drop is relatively more buoyant, the equilibrium position moves back to the centerline. The equilibrium position of the drop depends on the Froude number of the flow. The behavior has been investigated for various Froude numbers. The equilibrium position also depends on the drop deformation. When the Capillary number is raised, the equilibrium position moves away from the wall. At relatively large Capillary numbers, the drop shape is not stable, and the equilibrium position shows small oscillation due to an unstable drop shape. The effect of the Reynolds number on the equilibrium position has also been studied by a few simulations. It is found that at a relatively large Reynolds number and a moderate Froude number the drop oscillates with a finite amplitude inside the channel. The equilibrium position of the drop agrees qualitatively with perturbation theories and numerical results available for solid particles.Suspensions of buoyant drops at low and moderate and areal fractions are studied at non-zero Reynolds numbers in simple shear flow. The flow is studied as a function of the Capillary number, the Reynolds number, the Froude number and the density ratio. It is found that the effective viscosity decreases with Capillary number. The normal stress difference increases with Capillary number. The effective viscosity and normal stress difference also depend on the Reynolds number. In the dilute limit the normal stress difference decreases with Froude number and becomes negative at large Froude numbers. At a moderate areal fractionthe behavior of the suspension is nearly similar to the dilute case, except that the normal stress difference is always positive. Also the flow weakly depends on the Froude number at moderate areal fraction. The density distribution of buoyant drops across the channel is non-uniform. Keywords: Neutrally and non-neutrally buoyant drop, Shear flow, Density ratio, Capillary number, Froude number, Reynolds number, suspensions of buoyant drops.