Injection of a polymer solution is used in many applications to increase the viscosity of the water phase and therefore reduce the high mobility ratio during oil displacement in porous media. Experimental evidence has shown that the viscoelastic behavior of some polymer solutions may contribute to a better oil displacement at the pore-level, reducing the residual oil saturation. This pore-level behavior is not clearly understood. Modeling viscoelastic flow of polymeric solutions in porous media is extremely challenging. The macroscopic flow behavior is directly associated with the extensional dominant flow through pore throats that form the porous media. Accurate models should be able to describe the extensional thickening effect observed in the flow of dilute high molecular weight polymer solutions. The model developed in this work is based on the flow rate-pressure drop relationship of polymer solution flow through constricted capillaries that serves as a simple model of the geometry of pore throats. A two-dimensional capillary network model is constructed in order to obtain macroscopic parameters from upscaling of the microscopic behavior. In single-phase flow, results show the effect of different rheological parameters on the macroscopic flow behavior. To study a two-phase flow, a dynamic network model was developed. The results obtained provide a more detailed description of the oil displacement by the water phase.