After the Fukushima nuclear accident in Japan, whether the structural safety of the nuclear power plant (NPP) can be guaranteed under an earthquake has been of wide concern. Automatic seismic trip systems (ASTS) have been deployed in NPPs. There are generally two units or more double units on the one NPP site, and the vibration energy of the structure can certainly affect its adjacent structures through the soil, and there is energy transfer and conversion between adjacent structures. At present, the distance between two reactors of NPPs of different reactor types is generally 100–200 m (this distance is referring to the distance between the centers of two reactors, which is slightly different for different reactor types). In the past, seismic instruments were used in the ASTS and the setting of shutdown threshold, so the impact of only one unit was considered in the structural analysis of NPPs, and the interaction of two reactors through site conditions was not considered. In addition, as the site conditions of NPPs become more and more complex, it is necessary to consider the impact of one reactor structure on another reactor structure through the soil on the same site under an earthquake. In order to analyze the influence of structure–soil–structure interaction (SSSI), a three-dimensional refined finite element model of NPPs is established in this paper. The soil–structure interaction (SSI) is considered by using viscoelastic boundary. The seismic responses of different positions of the raft foundation and NPP structure, under the conditions of considering SSI effect (one reactor) and SSSI effect (two reactors), are compared. The influence of SSSI effect on the seismic responses of the raft foundation and NPP structure is revealed. It is proposed that SSSI effect should be reasonably considered according to the site conditions for the structural analysis of NPPs for the NPP ASTS.