Unless detailed inelastic analysis is utilised, high temperature codes base creep relaxation during a dwell period within a cycle on the start-of-dwell equivalent stress. The relaxation of the equivalent stress is then taken to be governed by a uniaxial creep law for the material being considered. Elastic follow-up is also included in such calculations. With this approach, only equivalent values of stress and creep strain rate are obtained and the stress multiaxiality is therefore assumed to remain at its initial value as the stress relaxes. Codes suggest that the stress drop is limited to a small fraction (typically 20%) of the initial equivalent stress to ensure that this assumption does not lead to significant inaccuracy. This paper reports creep relaxation results for a cruciform plate subjected to displacement-controlled biaxial loading. The initial biaxial loading ratio, the geometry of the cruciform plate and the value of the power in a power-law creep model are varied and these lead to variations in the elastic follow-up describing the creep relaxation. The biaxial stress ratio is generally found to change as relaxation occurs and a multiaxial ductility approach is used to evaluate the associated effect on creep damage accumulation. This is compared with the creep damage estimated by assuming relaxation is simply controlled by the equivalent stress with no change in multiaxial stress state during relaxation. For biaxial plane stress with one principal stress initially being negative, it is found that significant equivalent stress drops (up to about 40% of the initial value) can be allowed without the simplified equivalent stress approach becoming inaccurate. More care is required for positive stress biaxiality and the influence of multiaxial stress changes is found to depend on the initial stress biaxiality and the degree of elastic follow-up. The results will be used to propose improved guidance for simplified inelastic calculations.