Understanding the flow behavior of viscoelastic fluids in porous media is critical for optimizing enhanced oil recovery (EOR). Polymers such as hydroxypolyacrylamide (HPAM) are used to improve sweep efficiency in reservoirs and these polymers often exhibit elasticity. Surprisingly, recent experimental and field observations indicate that these viscoelastic polymers improve oil recovery up to an additional 20%, contrary to the conventional wisdom that polymers should have no impact on residual oil saturation. Here, we attaempt to understand effects of viscoelasticity on residual saturation in water-wet and mixed-wet porous media. Static and dynamic computational fluid dynamics (CFD) simulations of oil droplets in the presence of viscoelastic polymer are conducted in geometries representative of pore throats. Results show that additional forces on the oil droplet are present for fluids that exhibit elasticity over those that do not (e.g. water) and those forces become larger as the oil droplet approaches a constriction. It is also shown using dynamic simulations that the amount of deformation of the oil droplet is greatly affected by the elasticity of the displacing fluid. These results are promising and provide a theoretical foundation for the laboratory and field observations of reduced residual oil.