  As is well known, the extrusion rate of polymers from a cylindrical tube or
slit (a ``die'') is in practice limited by the appearance of ``melt fracture''
instabilities which give rise to unwanted distortions or even fracture of the
extrudate. We present the results of a weakly nonlinear analysis which gives
evidence for an intrinsic generic route to melt fracture via a weakly nonlinear
subcritical instability of viscoelastic Poiseuille flow. This instability and
the onset of associated melt fracture phenomena appear at a fixed ratio of the
elastic stresses to viscous stresses of the polymer solutionte
