Unsteady flow of polymer liquids following sudden imposition of pressure gradient or bulk velocity in a slit has been considered. Theoretical results, obtained by numerical methods, are based upon the Leonov constitutive equation. For a constant bulk velocity, predictions indicate an overshoot in the pressure before attainment of a steady‐state value. Depending on the bulk velocity, this overshoot may noticeably exceed the steady‐state value. The presence of a pressure overshoot has been observed in extrusion experiments. Theoretical and experimental results for a constant pressure gradient show a successive maximum and minimum in bulk velocity before reaching a steady‐state value. By using a rheo‐optical technique, the time‐dependent gapwise birefringence distribution has been measured following an imposed pressure gradient. The latter experimental results have been found to be in good agreement with theoretical predictions.