Elastic follow-up is a mechanical boundary condition lying between constant load and constant strain control. It exists in many engineering components operating at high temperature and can result in dramatically different creep stress relaxation and strain accumulation rates in a localized region of a component. We have performed creep tests under constant load, constant strain and elastic follow-up control on an aged (additional 22,000 hours) 316H austenitic stainless steel after service in a nuclear power station for 65,000 hours. Primary and secondary forward creep models with parameters derived from the constant-load data were able to describe constant-load creep adequately, but not able to predict stress relaxation and elastic follow-up. We show that this is because ageing has increased the constant-load creep strain rate significantly but has no effect on stress relaxation creep strain rate. Ageing promotes the formation of ferrite/chi phase at grain boundaries which are preferential sites for creep cavitation under load control. However, creep cavitation is less likely under constant strain and elastic follow-up control because a high creep strain rate, large creep strain and stress cannot coexist under these boundary conditions.