Monte Carlo calculation is used in the seismic risk analysis of infrastructures that consider various parameter uncertainties; however, the calculation cost increases as the parameters become higher in the non-linear time history analysis with seismic load input. In this study, we verified a surrogate modeling by the Gaussian process regression for the input / output relationships of the seismic analysis of a typical seismic isolated pier. By using a constructed surrogate model, the number of structural analyzes could be effectively reduced. Then, it was shown that the Automatic Relevance Determination (ARD) kernel can appropriately and automatically extract the degree of influence of the structural parameters on the maximum seismic response for the occurrence of different nonlinearities.