In order to describe viscosity function behavior dependent on shear rate in steady-shear flow and to predict the first normal stress function without using discrete relaxation time spectrum, we combined the microscopic entanglement concept based on Graessley’s entanglement network theory with the macroscopic constitutive model. The viscosity function derived from the entanglement, model has three adjustable parameters and it was assumed to have the form of the inverse cotangent function of the shear rate. Then the first normal stress function is obtained using the Wagner’s relationship. The model prediction for the first normal stress coefficient is compared with experimental data of polymer melts. Even though viscosity function and the first normal stress function vary over a wide range of shear rate, they were in good agreement for polymer melts at high shear rate. First normal stress function do not show any numerical artifacts. However, discrepancy in the first normal stress function occurs at low shear rate. This is due to the irreversibility of the entangled molecule’s motion that was not taken into consideration in the entanglement model. Irreversible nonaffine motion is introduced by adding a term similar to the White-Metzner model’s irreversible factor. Addition of irreversibility in the calculation of the first normal stress function considerably improves the agreement. Other comparisons are also presented and related discussions are given.