The num erical simulation of sedimenting deformable drops inside a vertical channel under gravity has been performed at finite Reynolds numbers. The three dimensional channel is confined in x-direction by two vertical walls and is periodic in y- and z-directions. Results are obtained using a finite difference/front tracking method. The main dimensionless parameters are Reynolds number, Bond number and ratio of the length of channel to the diameter of drops. The effect of these parameters on lateral migration of drops is investigated. In the case of one drop, the wall repulsion is the main mechanism of the lateral migration of the drop and centerline of the channel is the steady state equilibrium lateral position of drop. When the Reynolds number is below 60.0, two different lateral migration regimes are observed: migration with monotonic approach and migration with damped oscillations. These regimes are affected by dimensionless parameters. When the Bond number increases, the oscillations of drop around the centerline of channel are stronger and so the time required for damping these oscillations is longer. If the length of the channel in x- direction increases or the diameter of the drop decreases, drop is less influenced by the walls of channel. As a result, the oscillations of drop around the centerline of the channel are damped. Results of lateral migration of one drop are consistent with perturbation theory of Cox et al and two dimensional numerical simulations performed by Feng et al for solid circular cylinders. Drag coefficient also has been calculated and effect of various parameters has been discussed. It is found that drag on a viscous drop is different from rigid spherical drops because of two effects: effect of internal circulation of drop and effect of drop deformation. The internal circulation of drop is basically related to the viscosity ratio and is weaken by increasing the viscosity of the drop fluid or decreasing the viscosity of the ambient fluid. Generally the internal circulation of the drop, decreases the drag coefficient of the drop and according to the steady state shape of drop, deformation of the drop can increase or decrease the drag coefficient of the drop. Drag coefficient of the drop, is also affected by ratio of the length of the channel in x- direction to the diameter of the drop. If length of the channel in x- direction decreases or diameter of the drop increases, the drag coefficient will increase. In the case of two and four drops, drops are initially placed in tandom with a specific separation distance. The study of two drops is similar to that done by Feng et al for solid circular cylinders. In all simulations of two drops, drops finally get a symmetric configuration with respect to channel axis with equal spacing from the walls. The mechanism of interaction is basically same as that defined by Feng et al which is drafting, kissing and tumbling (DKT). As the Reynolds number or ratio of the length of the channel to the diameter of the drop increases, Drops move slightly towards the walls. This result is consistent with experimental results of Wu et al for two spherical particles sedimenting in a vertical channel. Depending on the ratio of the length of the channel in x- direction to the diameter of the drops, four drops sediment in two or four columns with the same settling velocity. Key words : Deformable drops, Lateral migration, Wall repulsion, Reynolds number, Bond number, Drag coefficient