Instabilities in polymer processing limit production rates and may influence the aesthetic or me- chanical properties of the final product. One example is the fountain flow instability, which takes place during the mold filling stage of an injection molding process. It has been shown experimen- tally that these instabilities manifest themselves in the form of a periodic oscillation of the flow front stagnation point between the two walls of the mold channels. The onset is determined by a critical Weissenberg number, the ratio of material response time scales to flow time scales. Different values have been predicted in previous work[1][2]. We use the finite element method and a number of stabilization techniques for flows of convective and viscoelastic nature (DEVSS-G/SUPG[3], LCR[4]) to do a full non-linear, transient simulation of a branched polymer melt propagating through a mold channel. We investigate the onset and behavior of the fountain flow instability with special focus on describing the contact point where the polymer is deposited on the mold wall. High stress and velocity gradients require special local treatment of the sharp interface method used to describe the free surface deformation. We observe the onset and behaviour of the flow during an instability. For low Weissenberg num- bers, we observe that the perturbation vanishes, indicating a stable system. For high Weissenberg numbers we observe oscillating behavior as the perturbation grows, as observed in experiments [6]. We investigate how varying material properties influences this critical Weissenberg number and the behaviour during unstable flow. This research forms part of the research programme of the Dutch Polymer Institute, project 788