Abstract: Design by analysis is one of the main methods for nuclear power equipment design. The structure integrity was judged using the safety-factor based on deterministic approach providing that safety margins of input parameters are sufficient in the design by analysis. In practical engineering, nondeterministic variables exist, such as geometry, material properties, occurrence of beyond design basic loads etc. Based on the design by analysis, the reliability and optimal analysis methods were introduced in the basic design or assessment by considering uncertainty of the subjective input variables (such as stress linearization paths). The transition cone of steam generator which is a typical structure of nuclear key component was chosen as a research case in this study. First, the sensitivity analysis was carried out to select the parameters which have the greatest influence on the stress linearization path, and then the best path was optimized by optimal analysis. The methods used in this study provide some suggestions for the selection of stress linearization path for engineering design. Meanwhile, these methods have a positive meaning to the application of reliability theory in the design by analysis of ASME codes and standards.