The kinetic theory of liquids has been used to derive two crude models which rationalize the establishment of a molecular weight gradient during the capillary extrusion of polydisperse thermoplastic melts. A molecular weight decrease near the polymer/die wall interface is predicted along with a decay in the degree of extrudate swelling with increasing die length, each model giving equations relating decay rate with die dimensions and shear rate. Polyethylene data indicate some shortcomings in the theory, but both models fit experimental extrudate swelling data well, and appreciably better than an empirical equation of exponential decay. Further in keeping with theory, surface sections of broad molecular weight distribution polyethylene extrudates have lower molecular weights than whole extrudates, the magnitude of the effect increasing with increasing die length. No significant molecular effect was found for a fractionated linear polyethylene. The decay in extrudate swelling was also found to be much greater for broad molecular weight polyethylene samples than for the fractionated polymer. It is suggested that molecular fractionation in capillary flow is a significant contributing cause to the difference in die length variation of melt viscosity and melt elasticity.