Abstarct: Investigation on two phase flow problem and particularly motion of droplets descending in another media is of great importance in medical fields (particularly production of penicillin), sedimentation reservoirs, water treatment industries (in sedimentation process of solids in water), heat exchangers and other problems in industry. In the present study, an analytical solution baxsed on the perturbation method is obtained to simulate the creeping flow and motion of a viscoelastic drop descending in another immiscible viscoelastic quiescent media. In different industrial application any of these media (interior or exterior fluids) can show non-Newtonian behaviors. For the sake of this reason a rigorous investigation on the scenario in which both fluids are non-Newtonian is carried out. The quasi-linear and non-linear Oldroyd-B and Giesekus constitutive equations are implemented for both interior and exterior phases due to theirs high suitability in simulation of polymeric solutions behaviors. The perturbation parameters are considered to be Deborah numbers defined baxsed on the corresponding relaxation times of drop and exterior fluids and capillary number to linearize the governing equations. To check the accuracy of presented solution an experimental part is also included to the current version of study. In the experimental part a solution of Polyacrylamide in water/glycerin is implemented as the interior viscoelastic phase. In previous studies Xantham gum were used in most of works that dues to its rigid molecular structure it was not to be simulated perfectly using the presented simple constitutive equations. Silicon oil is used as the exterior media which is a water repellence fluid. Also due to its high viscosity, it is a great choice in creep simulation scenario. In contrast to the generally spherical shape of Newtonian drop creeping in viscose media, it is shown that the effect of elasticity in this scenario can even feature prolate and oblate shapes. The results have shown suitable agreements with previously reported experimental results. The motion of the droplet in surrounding media is considered to be creeping. Effects of different parameters including Deborah numbers, elasto-capillary number, viscosity ratios of drop and exterior media and, viscosity ratio between the drop and external flows are rigorously investigated on the shape, motion, stream function and drag force of drop falling into quiescent media.