We examine the transient displacement of viscoelastic fluids by a gas in straight cylindrical tubes of finite length. For the simulation of the processes, the mixed finite element method is combined with a quasi-elliptic grid generation scheme for discretizing the highly deforming domain of the liquid and the discontinuous Galerkin (DG) method for calculating the polymeric stresses. In addition the effectiveness of other formulations is examined: streamline upwind/Petrov (SUPG), DG/discrete elastic viscous stress splitting (DEVSS), SUPG/DEVSS and the latter two also with the DEVSS-G approximation with either the PTT or Giesekus constitutive models. A parametric analysis is made in order to examine the effects of elastic and inertia forces and of the Newtonian viscosity on the process. Results using the PTT constitutive model show that the thickness of the remaining film increases as the Deborah number increases and that remaining fluid fractions greater than 0.60 arise, the Newtonian limit, in agreement with experiments. However, the thickness of the remaining film is not as large as with Boger fluids due to the shear thinning nature of the PTT fluid model. Moderate and high values of the Deborah number cause the development of extremely sharp stress boundary layers, which affect eventually the stability of the applied numerical scheme. Increasing the contribution of the Newtonian viscosity decreases the effects of the viscoelastic model. In particular, the bubble motion is decelerated, the thickness of the remaining film tends to the Newtonian limit and the polymeric stresses decrease in magnitude. In the fully developed region, well-ahead of the penetrating gas, the predictions for the distribution of upsilon(z), tau(zz), tau(rz) are in qualitative agreement with the semi-analytical work of [J. Fluid Mech. 387 (1999) 271]. (C) 2004 Elsevier B.V. All rights reserved.