In typical dynamic soil-structure interaction (SSI) problems, the dynamic response a structure can be affected by the existence of some nearby structures, which is sometimes referred to as the dynamic structure-soil-structure interaction (SSSI). This effect is especially important in the earthquake engineering design of adjacent nuclear power plants, as the safety risk is relatively high. However, the current understanding on the SSSI of nuclear power plants is still insufficient. In this work, we use the finite element method to investigate the SSSI of two nuclear power plants located at a specific distance under earthquake excitation. Four nuclear-power-plant-soil systems are designed to account for the SSI and SSSI respectively, where the soil properties are obtained from drilling data. The effect of the SSSI on the nuclear power plants is studied by comparing the dynamic responses of four nuclear power plants-soil systems in vertical and horizontal directions, in which both layered soils and local weak interlayer soils are considered. The results of numerical study show that the presence of one nuclear power plant has a favorable effect on the seismic response of an adjacent nuclear power plant, such as reducing the displacement response, but this effect is limited. In addition, the SSSI effect is related to not only the soil properties, but also the direction of ground motion. Furthermore, the existence of soft soil layers complicates the SSSI effect. The results provide important insights for the construction and expansion of nuclear power plants.