The dynamics of droplets and elastic capsules in a low Reynolds number flow is investigated by Front-Tracking method. The motions of droplets under gravity field, shear flow and Poiseuille flow are shown as examples. The capsules are migrated to the center line of the Poiseuille flow due to the lateral migration. The hydrodynamic conductance of the Poiseuille flow is reduced as the capsule goes to the center of the channel. The small capsules move to the boundary wall of the Poiseuille flow in the mixture of large and small capsules.