Oil recovery processes depend on many factors that can be altered in order to maximize the sweeping efficiency in porous media, and one of these is the rheology behavior of the displacing agent. Furthermore, scales in the recovery process should also be considered: from the macro- to microscale systems, in which capillary forces become predominant. It is also well-known the non-Newtonian behavior of polymer solutions used in Enhanced Oil Recovery (EOR) processes. This has been considered before, explaining how the polymer’s viscosifying properties enhance the displacing process. Recently, another property exhibit by polymer solutions started being considered: the viscoelasticity. The interaction between the (macro)molecules in the displacing phase generates a complex stress field which cannot be simply addressed by an increment in the shear viscosity. We present a 2D, multiphase simulation at macro- and microscale of a recovery process with different fluid models, showing that viscoelastic fluids increase the recovery performance due to the extra stresses generated by the polymer molecules, up to a 15.4% when compared to traditional waterflooding techniques. The viscosity of the displacing phase affects indeed the recovery efficiency, and moreover, the results also evidenced that not only the bulk viscoelasticity, but also the interfacial forces play a vital role in the microscopic sweeping efficiency in polymer EOR flooding processes. This can be used when determining the properties of future EOR agents to be synthesized.