This paper presents results from a numerical and experimental research programme motivated by the need to predict creep damage generated by multi-axial states of stress in austenitic stainless steels. It has been hypothesized that highly triaxial residual stress fields may be sufficient to promote creep damage in thermally aged components, even in the absence of in-service loads. Two prerequisites to test this hypothesis are the provision of test specimens containing a highly triaxial residual stress field and an accurate knowledge of how this residual stress field relaxes due to creep. Creep damage predictions may then be made for these specimens and compared to damage observed in experiments. This paper provides solutions to both of these prerequisites. Cylindrical and spherical test specimens made from type 316H stainless steel are heated to 850 °C and then quenched in water. Finite element predictions of the residual stress state, validated by extensive neutron diffraction measurements, are presented which confirm the high level of triaxiality present in the specimens. The specimens are then thermally aged at 550 °C and numerical predictions of the residual stress relaxation are given, again validated by extensive neutron diffraction measurements. The results confirm the validity of the creep relaxation models employed. In addition, the results show the influence of specimen size and permit comparisons to be made between three different types of neutron diffractometers.