It is proved that the statistical parameters of a random response can be directly expressed in terms of transfer function; and then a transfer function-based stochastic seismic response analysis is made on Baihetan underground caverns. The seismic reliability of underground caverns is also discussed. The results indicate that in addition to stochastic seismic response of the caverns

spectral characteristics of seismic response and seismic response estimations can be conducted at the same time

which leads to a more profound point of view in comparison with conventional methods. Results of stochastic seismic analysis and transfer function-based estimation are well consistent with the results of numerical computation. The theory of excursion failure criterion is firstly applied to provide a new approach to consider the randomness of earthquake loading in stochastic seismic response analysis of underground caverns.