By assuming that in a strong extensional flow a polymer molecule in dilute solution is quickly driven into a folded or kinked state in which drag and entropic elastic forces dominate over the Brownian force, we derive "kink dynamics" equations that describe the unraveling of the molecule in the extensional flow. Solving these equations numerically, we find that although the ends of the chain move, on average, affinely in the flow field until the chain is unfolded to about 1/3 of its fully extended length, large viscous stresses are produced because the solvent must flow around nonextending strands of polymer that lie between neighboring kinks. These predictions are compared with available experimental data and with other theoretical models. © 1990 Steinkopff.