We report here a computational study, with inertial contributions included, of the time-dependent velocity and shear stress profiles following flow start-up from rest for a polymeric liquid. Earlier workers solved similar fluid-mechanical start-up problems with viscoelastic character represented by a single Maxwell element. They found significant oscillatory departures from the steady-state velocity profile that persist throughout the entire period of stress growth to steady state. Such results are unsettling since they imply that the usual assumptions about velocity fields for transient tests of polymeric liquids are seriously in error. It turns out, however, that such oscillations are rapidly suppressed when a broad distribution of relaxation times is employed, the physically appropriate situation for polymeric liquids. The initial shear wave oscillations decay quickly compared with the time to reach the stress steady state when realistic descriptions of their viscoelastic character are employed. We note that a combination of inertial contributions with sparse relaxation spectra in fluid-mechanical modeling can lead to spurious velocity and stress field predictions for polymeric liquid flows.