The stability of a rapidly contracting self‐pinched discharge (fast pinch effect) is studied using three different models for the plasma dynamics: (a) the free particle model; (b) the snowplow model; (c) the shock wave model. For each model the growth in time of a small perturbation on a time‐dependent unperturbed solution of the equations of motion is obtained. It is shown that the free particle model and the shock wave model predict instabilities. The instabilities are rather mild, the instability times being of the order of the pinch time itself. The snowplow model predicts stability for the initial stages of the pinch, although instabilities probably develop later on.