Well‐defined, uniaxial extensional experiments were carried out using a new apparatus which appears to be well suited as a “primary standard” for such measurements on molten polymers over a significant range of experimental conditions. Results are reported for two materials whose rheological properties in shearing flows had also been determined precisely. A polystyrene having a broad molecular weight distribution and a low‐density polyethylene were chosen as representative test materials and were studied at 165°C and 150°C, respectively, over a decade of stretch rates between about 0.04 and0.69 sec−1.Very simple constitutive descriptions, which suffice in steady shearing flows, are shown to describe the stress‐strain rate‐time behavior of polystyrene in extensional deformations of substantial complexity, as well as in constant deformation rate experiments. In the case of polyethylene, on the other hand, a “strain‐hardening” phenomenon occurs during extension. This would appear to require, except at low strain levels, the use of constitutive equations which consider explicitly the evolving melt structure in order to avoid spurious predictions when the kinematics are changed.