The reasons for cessation of drawing and for the local fracture processes occurring in linear polyethylene near ultimate draw ratios, λmax, have been studied by broad-line proton NMR and scanning electron microscopy. As λmaxwas reached during drawing, the sample whitened and kink bands similar to those observed at deformation of low molecular solids were formed. The kink bands were clearly seen in the micrographs. As evidenced by NMR, the segmental mobility of chains in the amorphous regions is almost completely suppressed because of a sharp increase of the orientation stress near λmax(though the temperature of drawing is close to the melting temperature). This phenomenon of mechanical vitrification is regarded as a fundamental reason for cessation of drawing and for transition to the “solid-state” fracture mechanism. Quantitative estimates are given for formation of submicrocracks arising at boundaries of kink bands.