We investigate the transient viscoelastic behavior of weakly strain-hardening fluids in filament stretching devices during uniaxial elongation and following the cessation of stretching. The numerical results are compared with experimental observations on a concentrated shear-thinning polystyrene solution which is well characterized by a multi-mode Giesekus model. The finite element computations incorporate the effects of viscoelasticity, surface tension, and fluid inertia and the time-dependent moving-boundary problem is solved using the code POLYFLOW. A detailed comparison of multi-mode computations with single-mode solution is presented in order to examine the differences in the predicted viscoelastic behavior and the role of the fluid relaxation spectrum. The evolution in the transient Trouton ratio at different deformation rates is compared with experimental measurements and with the theoretical predictions of ideal homogeneous uniaxial elongation. Simulations of the filament stretching device using the multi-mode viscoelastic model demonstrate a significant improvement in the agreement between the predicted and observed extensional viscosity at short times. The computed Trouton ratio is also in good agreement with theoretical expectations for ideal homogeneous uniaxial extension, despite the strongly nonhomogeneous viscoelastic necking of the fluid column observed during elongation in the filament stretching device. Following the cessation of elongation, numerical simulations predict an interesting and complex evolution in the kinematics of the fluid filament. Initially the tensile stresses in the column relax in the non-linear form predicted theoretically, indicating that filament stretching devices can be used to monitor transient extensional stress relaxation, provided that the evolution of the tensile force at the end-plate and the filament radius at the mid-plane are carefully measured. However, at longer times after cessation of stretching, the local extension rate at the axial mid-plane begins to increase rapidly, leading to a ＇necking failure＇ that is greatly accelerated compared to that expected in a corresponding Newtonian filament. The calculations show that this unstable necking is not driven solely by the surface tension but also by the viscoelasticity of the fluid, and is coupled with significant elastic recoil of the material near the end-plates. The rate of necking in the column is a sensitive function of the extensional viscosity predicted by the constitutive model, in particular the magnitude and the rate of strain-hardening that occurs during uniaxial elongation. This phenomenon can also be simply and accurately described by an appropriate set of coupled one-dimensional thin filament equations that use the finite element computations to provide a suitable initial condition for the axial distribution of the polymeric stresses in the filament.