New equation for determination of the primary normal stress difference from viscosity curve is proposed, and the methods of calculations with the use of adequate viscosity models are discussed. Comparison of calculated and measured values of primary normal stress difference has shown that the proposed equation describes quite well experimental data but the calculations are not stable. For this reason, the proposed equation along with other equations of this type known from the literature was transformed into shear stress-dependent form. It was shown that such transformation makes it possible to represent the normal stress-to-shear stress ratio (Weissenberg number) as a unique function of the local slope of the flow curve, which is simultaneously temperature invariant. Such representation was confirmed using experimental data for eight systems comprising linear polymers and various measurement temperatures. It was found that new equation in the shear stress-dependent form is numerically stable and provides excellent description of experimental data. The general structure of expressions, which may be used for description of the elasticity of polymer liquids based on the flow curve shape, was discussed from the point of view of dimensional analysis. Obtained results made it possible to modify other expressions known from the literature in such way that they also provide an excellent fit to experimental data.