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In the recent past it has been found that a considerable pressure drop occurred during the extrusion of linear polyethylene in the course of capillary flow. The pressure drop resides within a narrow temperature window of one to two degrees Celsius. In this research the hydrodynamic condition and molecular origin of the extrusion window of linear polymer were investigated further. The advantage of the extrusion window, viz. smooth extrudate with less die swell ratio attained at low extrusion pressure and temperature, has potential in industrial applications. However, the extrusion window, corresponding to linear polyethylene (PE) with relatively low polydispersity (<7), has a narrow window temperature interval, circa 1~2°C, thus it could not be applied to industrial scale processing at the industrial scale. To have a fundamental insight and make the process industrially viable, research in this thesis was devoted to broaden the extrusion window to tolerate the thermal fluctuations in conventional processing. To achieve this goal molecular weight dependence of window temperature and flow criticalities is revealed. The hydrodynamic conditions of the extrusion window observed in a rate-controlled rheometer and stick-slip flow studied in a stress-controlled rheometer could be traced back to the same origin, viz. slip flow arises due to the disentanglement of adsorbed chains on capillary wall from free chains in the bulk. Secondly, a dual window effect was uncovered in the course of capillary flow of a bimodal PE, which is consistent with the window temperature dependence on molecular weight. Moreover, it was found that flow induced orientation within the window effect is even less than that observed in steady state flow at a relatively low shear rate. This implies that in the window region only relaxed free chains are extruded through the capillary die and most of the adsorbed chains, which could be disengaged from the entangled melt, remain sticking to the inner capillary wall. This observation is consistent with the hydrodynamic origin of high-surface-energy-die slip flow. Finally, a unimodal linear PE with extremely broad molecular weight distribution, i.e. polydispersity (PDI) is 27, showed a broad window effect, circa 8°C, at an appropriate apparent shear rate. The molecular origin of such a broad window effect is due to its broad molecular weight distribution. These results have further implications for energy efficient processing.