Unless inelastic analysis is used, high temperature codes base creep relaxation on the start-of-dwell equivalent stress, which relaxes according to a uniaxial creep law. Elastic follow-up is also included. This approach only evaluates equivalent stress and creep strain rate and the multiaxial stress state is assumed to remain at its initial value as the stress relaxes. Codes suggest that the stress drop is limited to a fraction (typically 20%) of the initial equivalent stress to ensure this assumption does not introduce significant inaccuracies. This article provides a numerical examination of creep relaxation of a cruciform plate subjected to displacement-controlled biaxial loading, with the aim to provide clarification of any required constraint on stress drop. The initial biaxial stress ratio, the plate geometry and the power in a power–law creep model are varied, leading to variations in the elastic follow-up describing the creep relaxation. The biaxial stress ratio is generally found to change with relaxation and a multiaxial ductility approach is used to evaluate the associated creep damage accumulation. This is compared with the damage estimated assuming relaxation is controlled by the equivalent stress with no change in multiaxial stress state. For biaxial plane stress with one principal stress initially being compressive and one tensile, it is found that significant equivalent stress drops (about 40% of the initial stress) can be allowed without the simplified equivalent stress approach becoming inaccurate. More care is required for tensile–tensile stress biaxiality where multiaxial stress changes 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.