A theory describing the influence of energetic trapped particles on resistive‐interchange‐ballooning modes in tokamaks is presented. It is shown that a population of hot particles trapped in the region of adverse curvature can resonantly interact with and destabilize the resistive interchange mode, which is stable in their absence because of favorable average curvature. The mode is different from the usual resistive interchange mode not only in its destablization mechanism, but also in that it has a real component to its frequency comparable to the precessional drift frequency of the rapidly circulating energetic species. Corresponding growth rate and threshold conditions for this trapped‐particle‐driven instability are derived and finite banana width effects are shown to have a stabilizing effect on the mode. Finally, the ballooning/tearing dispersion relation is generalized to include hot particles, so that both the ideal and the resistive modes are derivable in the appropriate limits.