By use of nonequilibrium simulations a coarse-grained model of polyethylene, developed in our previous work [J. Chem. Phys. 115, 2846 (2001); 117, 925 (2002)], is subjected to a planar Couette flow. Both transient and steady-state nonlinear flow properties are investigated for shear rates varying from 30 to 3000 µs–1 and chain lengths varying from C80H162 to C800H1602. We report rheological data (shear viscosity, normal stress differences) and structural data (chain dimensions and the order tensor), and compare them with experimental results, where available. The locations of maxima and magnitudes of overshoots in the shear stress and normal stress difference are in agreement with experimental results. We also observe an undershoot in the transient extinction angle and a decrease of the steady-state extinction angle with shear rate, both of which are in very good agreement with recent experiments. Two rheological "rules," the stress–optical rule and the Cox–Merz rule, are tested. It is shown that the extinction angle, as calculated from stress components, remains equal to the optical extinction angle even for high shear rates, where the stress–optical rule is no longer strictly valid.