The structural integrity of reactor components is very essential for the reliable operation of all types of power plants, especially for components operating at elevated temperature where creep effects are significant and where components are subjected to high-temperature alteration and seismic transient loading conditions. In this article, a molten salt storage tank in high temperature thorium molten salt reactor (TMSR) is evaluated according to ASME-III-5-HBB high temperature reactor code. The evaluation based on 3D finite element analyses includes the load-controlled stress, the effects of ratcheting, and the interaction of creep and fatigue. The thermal and structural analysis and the application procedures of ASME-HBB rules are described in detail. Some structural modifications have been made on this molten salt storage tank to enhance the strength and reduce thermal stress. The effects of ratcheting and creep-fatigue damage under elevated temperature are investigated using elastic analysis and inelastic analysis methods for a defined representative load cycle. In addition, the strain range and the stress relaxation history calculated by elastic and inelastic methods are compared and discussed. The numerical results indicate that the elastic analysis is conservative for design and a full inelastic analysis method for estimating input for creep-fatigue damage evaluation need to be developed.