When a steady viscous flow of a molten polymer is suddenly stopped, the stress τ can be recorded as a function of the time t. By means of inverse Laplace transforms, a system of linear Maxwell bodies relaxing in the same way can be defined. It is shown that the elastic energy WM stored within this system is equal to A/2, where is the rate of shear of the steady flow and where
is the “stress relaxation area.” Thus, for a calculation of WM the inverse Laplace transforms are not needed. Then, the following parameters are defined: (1) the shear compliance Jw, (2) the relaxation time λw of a single Maxwell body storing the same energy WM under the same steady viscous flow (λw is also equal to the double of the ratio of WM to the power dissipated in the steady flow), and (3) a “nonlinearity exponent of elasticity” given by the slope of the log-log plots of the Jw against the initial stresses. Stress relaxations in low- and high-pressure polyethylenes and natural rubber have been measured by means of a coneplate consistometer. The above-defined parameters are calculated and discussed as possible means of characterizing the polymer structure.