In the flow of molten high polymers through capillaries, an instability occurs at shear stresses 105∼108 dynes/cm2. The instability results in emerging streams of irregular shape. Several explanations of extrudate irregularities have been published up to the present, but they may be considered to be insufficient. In this paper, considering that the flow states of a viscoelastic fluid are governed by the elastic force, the viscous force and the inertia force, two dimensionless numbers Re* and NE are deduced. Then, it is verified by the experiment that the onset of instabilities in an extrudate of molten high polymers depends on these dimensionless numbers Re* and NE.