We have investigated the molecular origins of shish-kebab morphology occurring in polymer crystallization under extensional flow. Emergence of shish-kebabs is intimately related to the discontinuous coil-stretch transition of isolated chains. Our computed free energy landscape shows that there are in general two populations of stretched and coiled conformations at a given flow rate, even for monodisperse chains. While the stretched chains crystallize into shish, the coiled chains first form single-chain lamellae and then adsorb to the shish constituting the kebabs. We have followed the molecular details of formation of the shish and kebabs, and their dependence on initial configurations of chains, polymer concentration, and rate of crystallization. The local inhomogeneity in polymer concentration dramatically alters the population of stretched and coiled conformations, thus significantly influencing the onset of shish-kebab morphology. The propensity of kebabs is reduced by lowering the rate of crystallization and/or increasing the flow rate. (C) 2003 American Institute of Physics.