The Oldroyd-B, Giesekus, FENE-P, and White-Metzner models are used to predict the uniaxial extensional stress growth results of two ideal elastic fluids and a shear-thinning fluid. The model predictions are compared with the data obtained, at constant deformation rates, using the filament stretching technique. The linear viscoelastic parameters for the models were obtained by fitting the Oldroyd-B equations to the dynamic data. For the Giesekus and FENE-P models, the extra nonlinear parameters were obtained by fitting the model predictions to the steady shear data. The parameters for the White-Metzner model (using Carreau-type equation) were also obtained by directly fitting the steady shear data. For the ideal elastic fluids, Oldroyd-B, Giesekus, and FENE-P models with multiple modes of relaxation times generally provide good predictions of the extensional stress growth at small strain, but not particularly well at high strain. While the Oldroyd-B model predicts infinite extensional viscosity at finite extension rates, the Giesekus and FENE-P models predict steady extensional viscosities which are of the correct order of magnitude. The FENE-P equation also shows a more abrupt approach to steady state, similar to that observed experimentally. For the shear-thinning fluid the Giesekus and FENE-P models fail to predict the large stresses found in extensional flow. On the other hand, the White-Metzner model, while unable to predict the extensional stress growth for the ideal elastic fluids, is an improvement over the Oldroyd-B model for the shear-thinning fluid.