Results are presented from hybrid 2‐D quasineutral Darwin simulations of the interchange instability in the presence of a large rf wave in the ion‐cyclotron frequency range. The simulation models the plane perpendicular to the background magnetic field using cold particle ions and a cold E×B electron fluid. Related theory is also discussed. Fluid equations appropriate to the simulation model are derived and their properties demonstrated and compared to simulation. A method for solving for the rf‐modified growth rates from the fluid equations is described. It is generally expected that the current component associated with the mean, rf‐induced ion drift is capable of influencing the stability of the interchange mode; however, no modification of the mean ion drift is observed in simulations in which rf is present. Instead, in both the theory and simulation, an electron rf‐field oscillation current dominates the modification to the gravitational current. As a result, even in the presence of large rf fields (Brf/B0=15%), only modest corrections to the interchange growth rates are observed. The effect is stabilizing for kLn≲0.8–0.9, apparently for both signs of the square‐electric‐field gradient, and is destabilizing for larger values of kLn, although the credibility of the simulation begins to become suspect here. Fractional reduction of the interchange growth rate is observed to be quadratically dependent on the rf wave amplitude, independent of ion‐cyclotron resonant effects, and proportional to ∇B2rf/∇B20, consistent with an eikonal theory developed for the study of stabilizing effects on perpendicularly propagating fast Alfvén waves. The results also suggest that additional gradient‐independent stabilizing effects may be operative when kLn∼1. Finally, it is also observed that, while the rf wave has little effect on the interchange instability, the interchange mode strongly affects the rf wave, damping it significantly as the mode saturates.