For the first time, the viscoelastic flow front instability is studied in the full non-linear regime by numerical simulation. A two-component viscoelastic numerical model is developed which can predict fountain flow behavior in a two-dimensional cavity. The eXtended Pom-Pom (XPP) viscoelastic model is used. The levelset method is used for modeling the two-component flow of polymer and gas. The difficulties arising from the three-phase contact point modeling are addressed, and solved by treating the wall as an interface and the gas as a compressible fluid with a low viscosity. The resulting set of equations is solved in a decoupled way using a finite element formulation. Since the model for the polymer does not contain a solvent viscosity, the time discretized evolution equation for the conformation tensor is substituted into the momentum balance in order to obtain a Stokes like equation for computing the velocity and pressure at the new time level. Weissenberg numbers range from 0.1 to 10. The simulations reveal a symmetric fountain flow for Wi = 0.1-5. For Wi = 10 however, an oscillating motion of the fountain flow is found with a spatial period of three times the channel height, which corresponds to experimental observations. (C) 2010 Elsevier B.V. All rights reserved.