The long‐standing problem of polymer melt‐flow instabilities is looked upon from a new and quite general mathematical viewpoint. A single mathematical model is developed allowing the macroscopic description of measurable state variables characterizing the different melt‐flow instability regimes. Based on the theory of relaxation oscillations, a set of two coupled first‐order ordinary differential equations, relating state variables—pressure and flow rate—provides sufficient degrees of freedom to describe all the relevant flow regimes in shear flow. By means of this model, the appearance of extrudate distortions can be expressed in terms of pressure and output fluctuations without the need to invoke a microscopic theory. The analysis contains the potential for practical melt‐flow instability predictions.