Material degradation and crack growth affect the residual service life of high temperature components used in power plants and aerospace industry. In this study, we present a predictive multiscale continuum damage model to account for the effects of creep, fatigue and oxidation on the damage evolution and crack growth behaviour of 316H stainless steel at 650 °C. The model is used in finite element predictions of mode I crack growth which explicitly considers the polycrystalline microstructure near the crack tip of a compact-tension specimen loaded in creep and fatigue at high temperature. The predicted crack growth rates are found to be in good quantitative agreement with measurements and with the bounds predicted by the approximate multiaxial ductility model. We discuss the relative importance of creep, fatigue and oxidation on the damage evolution in different loading regimes.