Motion and deformation of the drop falling in an immiscible fluid has become a benchmark problem in fluid mechanics and has a wide range of application in petroleum, medicine processing, metals extraction, power plant and heat exchanger. In this paper, an exact analytical solution of a falling viscous drop at low Reynolds number is investigated. Analytical solution for both internal and external flows is obtained using the perturbation method. The Reynolds numbers and capillary are considered as the perturbation parameters. Drop’s shape remains spherical for sufficient small ones. The falling drop’s shape at Newtonian phase, deforms from its spherical shape as its volume increases. Inertial forces, surface tension, normal components stresses have the most influence on the falling drop’s shape. Drop’s deformation is due to the forces at the interfaces acting between two fluids. By volume increase of the falling drop, normal components stresses overcome to the surface tension and cause a dimple at the bottom drops in addition to the inertial force enhancement. For small non-dimensional parameters (Reynolds number and capillary) drop’s deformation is exactly similar to a sphere and then by increase in Reynolds number and capillary, the drop’s shape alters and cause a dimple at the bottom drops. Analytical solution show suitable agreement in terminal velocity and drop shape estimation with experimental results.