A method of recovering oil embedded in an underground matrix adjacent a depleted oil reservoir includes injecting a mixture of polymeric material into the depleted oil reservoir through an injection borehole, applying a pressure to the mixture to free the oil from the matrix and move the oil towards a production well, and drawing the oil from the depleted oil reservoir through the production well. The method additionally includes modeling a shear thickening of the polymeric mixture and an onset of the shear thickening. The model can be incorporated into commercial numerical simulators for predicting the injectivity and recovery due to viscoelastic thickening independently and thereby assist in quick screening polymers for oil recovery applications.