Abstract Elves are transient luminous events appearing above thunderclouds. They are produced by high peak current lightning events. They occasionally appear as doublets or in general as multiplets. We model elves doublets by setting the temporal and spatial variations of the return stroke current amplitude and we show that our modeling results are consistent with the measurements by Pierre Auger Cosmic‐Ray Observatory. We show the normalized electric fields and the emission rates at the altitudes of elves and we discuss the ability of our model to simulate the time separation of elves rings in doublets for different return stroke parameters. Our model can explain observations which are not compatible with the typical concept of elves doublets being generated by ground reflections of waves generated by intracloud currents.