The elongational flow behavior of dilute polymer solutions is of great current interest because it has been suggested that elongational viscosity effects may be involved in a number of phenomena such as turbulent drag reduction and flow cavitation suppression. Unfortunately, recent experiments, in trying to investigate elongational effects, have produced widely varying results. In this paper, an attempt is made to analyze one of the factors that contribute to this diversity. By using a generalized convected Maxwell model, it is shown that in a transient elongational flow, both stretching rate and flow time must reach the proper values before high stress levels can be observed. This is true for both accelerating flows such as through a cone or wedge and decelerating flows such as in a free jet. Since most previous experiments have not considered flow time, consistent results cannot be expected. Consequently, the proper control of all flow conditions is an essential requirement when trying to observe high stress levels. The results presented here provide valuable guidelines in this regard.