This work delineates the molecular mechanism and various characteristics of a remarkable elastic yielding phenomenon observed in cold drawn ductile polymer glasses including poly(2,6-dimethyl-1,4-phenylene oxide) (PPE), bisphenol A-polycarbonate (PC), poly(ethylene terephthalate) (PET), and poly(methyl methacrylate) (PMMA). Elastic yielding occurs when a sizable retractive stress appears from a cold-drawn polymer glass (stored in stress-free state for days after unloading) during annealing above the storage temperature T-st that is still well below the glass transition temperature T-g. The induction time characterizing the emergence and buildup of the retractive stress to a level of sigma* above 10 MPa and the magnitude of sigma* both depends on T-st and the cold drawing temperature T-cd as well as the annealing temperature Tel-yieid. It is asserted that there is significant chain tension in the load-bearing strands (LBSs) of the chain network, produced during cold drawing of these ductile polymer glasses. The chain tension is preserved by the vitrification during storage and can drive the glass to undergo localized yielding. Upon "thawing" the segments surrounding LBSs, the chain tension can transmit across the chain network to show up as macroscopic retractive stress.