To study the dynamic response of a saturated sand-underground structure system subjected to earthquakes, a series of shaking table tests with a geometric scale ratio of 1/30 were conducted. Based on the experimental acceleration records of testing soil deposits, the relationship between dynamic shear stress and horizontal soil displacement was analyzed by the 1D shear beam inverse calculation method. Meanwhile, the development law of the equivalent dynamic horizontal subgrade reaction coefficient and the dynamic strain of the sidewall in the underground structure has also been discussed. The testing results indicate that the dynamic shear stress of the soil deposit under the bottom plate of the underground structure is larger than that of the soils surrounding the sidewall and above the roof plate; in addition, the soil displacement tends to decrease with the buried depth. The dynamic shear stress–displacement hysteretic loop of the soil deposits tends to be plump as the input amplitude increases. The spectral characteristics of ground motions obviously influence both the dynamic shear stress–displacement hysteretic curve and the excess pore water pressure ratio of saturated sand soil, especially under medium and strong excitations. The equivalent dynamic horizontal subgrade reaction coefficient decreases with the increase of soil depth, and the difference between the coefficient above and underneath the underground structure model can reach 7.589 MN/m3. On the contrary, the equivalent dynamic horizontal subgrade reaction coefficient decreases with the increase of the input amplitude of ground motions, and the maximum reduction ratios of the coefficient are 74.4%, 66.7%, and 47.3%, corresponding to the El-Centro, Kobe, and Wolong ground motions, respectively. The soil liquefaction has a certain effect on the equivalent dynamic horizontal subgrade reaction coefficient. In general, the dynamic strain at the top of the sidewall in the underground structure is higher than that at the bottom of the sidewall, which illustrates that the deformation of underground structures is in good agreement with the seismic deformation mode of soil deposits.