Abstract: The lateral supports of reactor pressure vessel (RPV) are expected as a major contributor to the seismic risk of high temperature gas-cooled reactor (HTR) and are crucial to the safety of HTR RPV under seismic events. In this paper, we focus on the identification of seismic fragility variables, the analysis of reasonable factor values of fragility variables, the calculation of High Confidence Low Probabilistic Failure (HCLPF) Capacity and seismic fragility Curves, the selection of the key parameters among fragility variables, and the exploration into the sensitivity of HCLPF to these key parameters of seismic fragility analysis. The results show that the HCLPF of lateral supports is much higher than the design basis earthquake level and that it is insensitive to the variability of the key parameters.