A numerical method for calculating the rheological behavior of polymeric liquids from their molecular models is presented

and several dumbbell models of polymer molecules are then calculated in terms of this method. Answers are given to some problems which could not be solved theoretically. The calculated results indicate that the dumbbell models can be used to simulate the rheological behavior reasonably well once the finite extension of molecules and non-linearity of intramolecular forces arc included in the models

and that the configuration-dependent coefficient of friction included in the FENE dumbbells can only change the flexibility of molecules when elongated

but cannot result in the "S"-shaped curves of elongation viscosity

and that inclusion of the hydrodynamic interaction in the Hookean dumbbells does improve its capability of simulating the rheological behavior of polymer liquids. The numerical method has showed new light on the molecular theory of polymer rhe-ology

and will possibly be used in the numerical simulation of complex flow to replace the constitutive equations of continuum mechanics by molecular models.