Tungsten thin films are deposited with a triode sputtering system in order to obtain an absorbing layer for X-ray masks. The mechanical stress is studied as a function of different pressure and RF power conditions during deposition. Rapid thermal annealing at different temperatures and durations is performed in order to produce films under low compressive stress. We observe that the stress changes occur over the time scale of seconds at the annealing temperature and that the corresponding activation energies are low (60 meV). Grain growth in a preferred orientation explains the observed changes in stress. The magnitude in the change of stress is in good agreement with a model proposed by Hoffman et al. relating the stress to grain size and grain boundary dimensions.