Abstarct: Motion and deformation of the drop falling in an immiscible fluid has a wide range of applications in petroleum, medicine processing, mextals extraction, power plant and heat exchanger. In this paper, an analytical solution of a falling viscoelastic drop at low Reynolds number is investigated. Analytical solution for both internal and external flows is obtained using the perturbation method. The Reynolds numbers, Deborah and capillary are considered as the perturbation parameters. The Oldroyd-B model is used as the constitutive equation. In part experiment, we use an immiscible drop of 0.01% polyacrylamide (PAA) in 80:20 glycerol/water falling through 339 cP polydimethylsiloxane oil. The drop’s shape remains spherical for sufficiently 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 of viscoelastic stresses have the most influence on its 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 of viscoelastic 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, Deborah and capillary) drop’s deformation is exactly similar to a sphere and then by increase in Reynolds number, Deborah and capillary, the drop’s shape alters and causes a dimple in the bottom drops. Analytical solution show suitable agreement in terminal velocity and drop shape estimation with experimental results.