Nuclear power reactors contain large steel pressure vessels and high-pressure pipework which must be carefully designed and regularly inspected when they are service to guarantee safety. When a reactor is operating, these systems are loaded not just by internal pressure, but also by thermal stresses which arise from temperature gradients, and by residual stresses which are 'locked-in' during construction. Thermal and residual stresses are often termed 'secondary' stresses and they are generally more difficult to measure and predict than the stresses which result from directly applied forces. Often, this means that parts which are in fact safe are pre-emptively taken out of service due to secondary stress concerns, incurring large costs in addition to plant downtime. In this project, new techniques will be developed to accurately predict how complex and multi-axial secondary stresses in components behave as they are further stressed in-service. This will require the development of a generalised mathematical framework to describe multi-axial stress relaxation, along with new computational methods to enable the analysis of complicated real-world structures. The predictive accuracy of the new analysis techniques will be tested in a series of experiments using neutron and synchrotron diffraction to observe how residual stresses deep inside metallic components change as they are subjected to changing external loads. The analysis techniques developed during this project will be integrated with existing structural integrity assessment procedures, allowing them to be readily used in industry, and leading to cheaper and more reliable power plants.