A Rheometrics mechanical spectrometer was modified to study the elongational properties of polymer melts. A prime concern is that the elongation be uniform so that the microscopic stretch history of fluid elements in the polymer rod will be independent of axial position. By sequential photographic techniques, the conditions under which a constant stretch history is achieved were determined quantitatively in terms of the Weissenberg number,ε̇τm.For Weissenberg numbers much greater than unity, a polymer's response is largely elastic, and uniform stretching is observed. For Weissenberg numbers less than unity, the response of a polymer melt is largely viscous, and uniform stretching is observed only for very small strains. The evaluation of the Weissenberg number for the specific test conditions should serve as a simple guideline for estimating nonuniform deformation conditions.