A tuned cavity rotating detonation combustion system includes a an annular chamber having an inlet and an outlet; a valve plate at the inlet of the annular chamber and comprising a plurality of openings spaced circumferentially around the inlet; a plurality of tubes each having an open end in communication with a corresponding opening of the valve plate and a closed end forming a tuned cavity, and a first opening between the open end and the closed end for injection of air; and a plurality of fuel injectors corresponding to the plurality of tubes, each fuel injector being configured to inject fuel into the tube between the first opening and the open end. Each of the tuned cavities has a length sized to resonate at a same frequency as a continuous detonation frequency of at least one detonation wave in the annular chamber. Alternately, or additionally, a plurality of flame arresters corresponding to the plurality of tubes are configured to arrest the at least one detonation wave generated in the detonation chamber from travelling into the tube.