To address the optimization design problem of the bursting performance of reverse-arched bursting discs (RABDs), a hierarchical Kriging (H-Kriging) surrogate model was constructed based on both high- and low-fidelity finite element analysis results. This model enables the rapid prediction of the burst pressure of RABDs, facilitating the development of a mathematical model for performance optimization and structural improvement. The results show that the H-Kriging surrogate model relating burst pressure to structural parameters based on high- and low-fidelity finite element models can significantly reduce computational cost while accurately predicting the burst pressure of RABDs. For the initial structural design scheme of RABDs, optimization was carried out using a genetic algorithm, with the optimized design accounting for manufacturing tolerance in disc thickness. This resulted in a 58.8% reduction in burst pressure fluctuation, significantly reducing the sensitivity of burst pressure to thickness manufacturing errors and providing valuable engineering reference.