To describe the nonlinear behavior of polymer melts and solutions with few parameters, a simple model for the shear viscosity function is proposed and applied to the first normal stress coefficient prediction using Wagner's relationship. Its prediction was compared with experimental data for seven polymer melts and four solutions. The nonlinear form of the model correlates very well with the experimental data over many decades of shear rate. From the correlation, the damping constant of Wagner's equation was obtained and its values were compared with Wagner's optimized values. Its agreement with previous results shows that it can be applied to model polymeric fluid behavior. The current model has some additional merits when compared to the finite series approach of Wagner. The proposed model also describes the elongational viscosity very well. Possible applications are discussed.