Elastic follow-up represents a boundary condition that lies between constant load and constant strain control (stress relaxation). This condition is known to exist in many engineering components operating at high temperature. The subject of this dissertation is the study of creep stress relaxation with and without elastic follow-up in 316 Type austenitic stainless steel at 550°C, involving the design and development of a new experimental test system based on a three bar model. The mechanical response and elastic follow-up in the three bar model is fully described in order to provide the fundamental theory for the following experimental design and data analysis. Three test rigs (Rig 1, 2 and ENGIN-X rig 3) were designed and built to conduct conventional stress relaxation tests with different values of elastic follow-up factor. The ENGIN-X rig 3 can also be used in the EN GIN-X neutron beam line with the purpose of observing the evolution of the lattice strains at different crystallographic planes under different loading conditions. The experimental results illustrate that the presence of elastic follow-up decreases the stress relaxation rate and introduces additional strain accumulation in the specimens. Our short term neutron diffraction measurements show that the intergranular stresses between different grains families remain constant during the tests irrespective of the degree of elastic follow-up, and elastic follow-up has no effect on the redistribution of lattice strains. In addition, a group of creep laboratory and an in-situ neutron diffraction anelasticity tests were conducted to study the effect of applied stress and creep history on internal stress. The creep laboratory anelasticity tests show that the internal stresses are proportional to the applied stress, and are only slightly influenced by the creep deformation. The in-situ neutron diffraction anelasticity test shows that the intergranular stresses between different grains families may contributed to anelasticity partly. A number of creep stress relaxation models were developed and based on the RCCMR creep equation and average creep rate law in order to predict the stress relaxation and elastic follow-up behaviour. The corresponding constants in the models were obtained from constant load creep tests. The predictions show that the RCC-MR strain hardening or differential strain hardening models with considering of global creep strain in specimens gave the best prediction. It was found that the consideration of internal stress in a model did not improve the prediction due to the incomplete understanding of the internal state during creep.