A diffusion-based coupled oxidation, intergranular damage and multisite randomised crack growth model for environmentally assisted oxidation/carburisation and creep time dependent material is proposed. A combined grain boundary and grain mesh structure is employed for simulating surface hardening and intergranular cracking resulting from a surface gas/solid carbon diffusion and bulk creep interaction by assuming variations in their strength ratios. Using 316H properties at 550° C the predicted surface intergranular cracks, due to both carburisation and creep, and subsequent crack growth are analysed in terms of their rupture and failure strains are compared to as received 316H data to validate the model.