This work concerns extension induced crystallization of a commercial high density polyethylene above the equilibrium melting temperature. We compare the nonlinear response during uniaxial elongation to the morphology obtained in the quenched fibers after cessation of the flow at a Hencky strain of 5. At 12 °C above the melting temperature, the samples undergo brittle fracture. Samples stretched at 2 and 6 °C above the melting temperature remain intact throughout the entire course of deformation and exhibit a strain hardening behavior that does not follow time temperature superposition. We propose that stabilization of the filament at lower temperatures, as well as the failure of time temperature superposition, is caused by flow-induced nucleation and growth of shish structures oriented along the flow direction. Further justification is obtained from small-angle X-ray scattering performed on the quenched filament showing an increased formation of shish with an increase in the deformation rate. We find the critical Hencky strain for the onset of the shish formation to be between 0 and 0.6, which is significantly lower than the values reported in the existing literature. We model the influence of shish nucleation on the rheological response in an extension using the hierarchical multimode stress function, which is modified to include the stretched network assumption.