The transient extensional viscosity function of two semi-dilute polyisobutylene polymer solutions is investigated in a filament stretching rheometer of the type developed by Tirtaatmadja and Sridhar (J. Rheol., 37 (1993) 1081). A velocity compensation algorithm which yields a constant deformation rate at a single point in both Newtonian and non-Newtonian fluid samples is detailed. Good experimental reproducibility is obtained in the device and measurements with a viscous Newtonian oil yield steady-state Trouton ratios of <(eta)over bar>/mu = 3 +/- 0.5. Both viscoelastic fluids show the onset of significant strain-hardening for Hencky strains greater than two, and transient extensional viscosities that increase by three orders of magnitude. Good agreement between the results for the two different fluids is obtained when tests are performed at identical values of the Deborah number. The maximum Hencky strain achievable in the device is epsilon = 5 and steady-state values of the extensional viscosity are never achieved over the range of strain rates attainable. Measurements show that the evolution of the tensile force exerted by the deforming filament is a strong function of the initial aspect ratio of the cylindrical test sample. A lubrication analysis for small sample aspect ratios demonstrates that this variation results from large radial pressure gradients arising from the non-homogeneous shear flow near the rigid disks. This simplified analysis provides a good description of the experimental observations, and tests conducted with the Newtonian oil suggest that only at Hencky strains epsilon > 2 does the extensional deformation of the filament dominate the shearing flow. In the case of viscoelastic fluid filaments, the initial shearing motion near the fixed endplates significantly affects the measured tensile stress in the filament at all later times in the extension. Careful attention is focused on the non-homogeneous deformation induced at the endplates that constrain the fluid sample at each end of the test apparatus. Measurements of the filament profile and surface curvature with a video-imaging system show distinct differences in the evolution of Newtonian and non-Newtonian samples. In both cases, different strain histories are experienced by fluid elements at different axial positions in the filament, and a spatially homogenous deformation is not achieved in the viscoelastic filaments until Hencky strains epsilon > 4 are attained. Observations at larger strains and high Deborah numbers, De > 3, indicate the onset of an elastic instability near the stationary endplate which results in the deforming fluid column partially decohering from the endplate.