The fiber-windup technique, developed by Macosko and Lorntson [SPE Tech. Papers 19, 461-467 (1973)] for rotational shear rheometers, was re-examined to obtain transient uniaxial extensional viscosity data. Macosko and Lorntson used a special force transducer to measure the tension in the filament being pulled. In contrast, in this study commercial rotational shear rheometers (Rheometrics Mechanical Spectrometer-800 and Rheometrics Fluids Spectrometer-II) with torque transducers were used to obtain the extensional viscosity. One end of the sample is clamped, while the other end is wound around a drum at a constant rotational speed, to achieve a given extension rate. Tests were conducted with a polyisobutylene sample at room temperature to verify reproducibility and were compared with published studies. Results for polyisobutylene and IUPAC-X low density polyethylene were found to be in good agreement with published results. Hencky strains of up to 6 could be achieved. The technique can provide valuable extensional viscosity data for high viscosity liquids.