The problems of uniform extension of liquids under constant strain rate and constant stretching force have been studied using a nonlinear rheological theory that describes the effects of finite elastic strains in viscoelastic liquids, with provision for the influence of deformative orientation on a scalar relaxation time. It has been shown that the predictions of the theory are in rather good agreement with numerous data for the extensional flow of polyisobutylene, even without taking the deformative orientation into account, (however, in cases where the latter was important it was considered in detail). Some new results for the extensional properties of polyethylene melts, as well as those from the literature, show that its behaviour is qualitatively different from that of polyisobutylene. The mathematical description of the extensional flow of polyethylene has to take into consideration the mechanism of flow thermoactivation and, apparently, an accumulation of ruptures of macromolecules in addition to the deformative orientation phenomenon.