Continuum damage mechanics (CDM)-based constitutive equations are reviewed and presented for austenitic AISI 316H stainless steels, which undergo creep deformation and damage at 550C. Two multi-axial stress rupture functions/criteria have been utilised. Equations and the finite element computer code, DAMAGE XX, were used to carry out CDM studies of the weldment in an axi-symmetric equivalent of the flank section of a pressurised superheater header at 550C. Damage and lifetime predictions were made using finite and small deformation solution techniques; an insignificant difference was observed. It is shown that, using appropriate mesh refinement techniques and selecting suitable weld material ductility, CDM can be used to predict damage initiation and growth and, subsequent creep crack growth due to reheat cracking. Predicted damage initiation and growth modes are shown to correlate well with experimental and in-service observations. The results highlight the importance of multi-axial stress rupture criteria and underscore the need for more accurate materials data, under the relevant multi-axial stress states, on well-characterized material batches. Also, ductilities of the different material phases of the weld, strain affected zone, fusion boundary and weld materials, are shown to play an important role and, therefore, require more accurate determination. It is concluded that a more precise determination of the mechanical properties is necessary if the governing physical mechanisms of reheat cracking and the conditions for possible crack arrest are to be understood.