A theory is presented for the self‐maintained transverse oscillations which arise in a low‐velocity jet as it plays upon an obstacle, thus generating edge tones. It is assumed that transverse forces act on each particle of the jet as it travels toward an obstacle, and that this force is due to “sources” of hydrodynamic origin localized near the obstacle. The law of motion is set up in the form of an integral equation involving unknown functions for the force field. It is shown that a number of important properties of jet‐edge systems, and of the edge tones they produce, can be deduced from the equation, even for highly simplifying trial assumptions about the unknown functions.