We simulate the rapid extension of polymeric filaments between parallel plates with special attention to the role of surface tension in the symmetry breaking azimuthal instability that may occur near the end plates. The instability is viewed as a precursor to the breakup into separate fibrils and the eventual elastic decohesion of the filament from the plate, it is demonstrated that high Deborah numbers are needed to initiate the instability and that surface tension provides a wave number selection. Moreover, the surface tension has a stabilizing effect on the end plate instability. (C) 2001 The Society of Rheology.