In this paper we study the transient elongational viscosity of a PIB/PB Boger fluid (fluid B) by performing both experiments and model calculations. The experimental results have been obtained by using a filament stretching device was described by van Nienwkoop and Muller von Czernicki (J. Non-Newtonian Fluid Mech. 67 (1996) 105-123). We have been able to obtain large strains, up to a Hencky strain of 8. A plateau for the Trouton ratio of close to 10(4) is found while approaching a strain of 8. The plateau value appears to be independent of the strain rate history. The predictions using various multi-mode constitutive models (Giesekus, FENE-P, Hinch, FENE) show that the FENE model is the only model which predicts values for the Trouton ratio that are very close to the experiments for the whole range from strain 1 up to 8. The predictions of the models are computed with the actual strain rate (epsilon) over dot (t) as determined during the experiments in the middle of the filament. During relaxation, both the FENE-P and the FENE model perform well. In order to be able to make predictions without carrying out the relatively expensive FENE calculations, we have developed a new closed form constitutive equation. The model is based on the dumbbell theory in which the connector force used leads to a viscous stress term. The predictions of the model in transient extensional flows are very good and comparable to the FENE model.