A model for the growth of a grain boundary crack in thermomechanical fatigue is derived for a single-phase or low alloy fcc metal at homologous temperatures near 0.5. Crack growth is hypothesized to proceed through vacancies binding in pairs at the crack tip to impurities or an oxide layer. This model is applied to 97Pb−3Sn, and the results compared with experiment. Good agreement is shown between the model and experiment, especially in predicting the effects of frequency and thermal-mechanical phasing. These effects do not appear to have been previously modeled successfully.