Using minimal formalism, we demonstrate that the massless photons, constituting the radiation in a cavity, contribute to the mass of the cavity in agreement with Einstein’s mass–energy formula. We assume that a photon has energy and momentum related to frequency byE=hν,p=hν/c. Restricting velocities to nonrelativistic values, we impart a uniform acceleration to the cavity. Reflection from a moving mirror produces a Doppler shift, and thus the momentum delivered to the front and rear walls can easily be calculated in the laboratory frame. A simple application ofF=maleads to the usual conclusion that the mass of a gas of photons of total energyUisU/c2. An alternative argument based on calculations in the co‐accelerating frame is also given.