Previous experimental studies of the polymer behavior in a starve fed single screw extrusion process have shown that contiguous solids melting mechanism which is observed for flood fed extrusion was not observed for starve fed extrusion. A new two-stage physical model of polymer melting in a starve fed single screw extrusion has been proposed with conductive mechanism for melting in the partially filled region and dispersed melting mechanism in the fully filled region. Mathematical models have been proposed for melting in both those regions. The models have been validated experimentally.