The analysis of motion and deformation of a drop falling into another immiscible media finds a wide range of applications, including, wastewater treatment using flocculation technique, petroleum engineering, medicine processing, metals extraction and heat exchangers. This paper presents an analytical solution based on a triple perturbation method, for cases in which viscoelastic drops are falling in another immiscible Newtonian media at low Reynolds numbers. Here, the Reynolds, Deborah and capillary numbers are considered to be the perturbation parameters. Moreover, an experimental investigation is carried out, which is also used to validate and extend the analytical data. Motion and deformation of immiscible drops of 0.01% polyacrylamide (PAA) in 80:20 glycerol/water falling through polydimethylsiloxane oil are studied, and this shows a good agreement with the presented analytical solution. It is shown that the viscoelastic drops remain spherical when the drop size is small - this corresponds to the domination of the capillary force. It is shown that as the volume of the droplet increases, normal components of the stress tensor exhibit a non-uniform distribution at the interface of the two fluids. Consequently, this can cause a dimple at the rear end of drops, depending on the magnitude of the surface tension force.