An adaptive controller was designed to handle the uncertainty of the payload's inertia, and the impact of the vibration isolation system on the satellite's attitude and stability was evaluated. They further proposed a 6-DOF isolation platform based on magnetic levitation actuators and investigated the electromagnetic coupling effect of the magnetic platform. They numerically verified the effectiveness of the platform for vibration isolation of the payload. It is also reported that the Stewart platforms have achieved active vibration isolation on the Worldview-II and Chandra X-ray observers [30]. Active isolation platforms typically have controllers and actuators, making them more complex than passive ones. As a result, they are typically only used to isolate effective payloads [31; 32]. For instance, the Tascat2 satellite launched by the United States in 2006 featured an active and passive combined isolation device installed on its camera [33]. On the other hand, passive isolation platforms are typically employed for flywheel vibration isolation [18]. In the aforementioned research on flywheel vibration isolation, researchers committed to improving the vibration isolation efficiency of the vibration isolation platform itself. However, their investigations have been limited to the premise that the flywheel platform is mounted on a rigid foundation. In practical engineering applications, the flywheels and isolation platforms are typically installed on an elastic foundation, such as a honeycomb structural plate with limited stiffness in the case of satellite structures. Unfortunately, there is a lack of research on whether a flywheel vibration isolation platform designed with a rigid foundation can achieve an equivalent isolation effect when installed on a flexible foundation. Therefore, in this study, the structural plate and the flywheel vibration isolation platform are treated as a plate-isolator system, and the influence of the structural plate's elasticity is investigated. It is reported that linear boundary damping can reduce the vibration energy of stiffened plates in the specific frequency band [34]. Thus, in this study, to further suppress the disturbance of flywheels, an elastic boundary is designed for the plate-isolator system, and the plate-isolator system with an elastic boundary is verified by a simplified analytical model and numerical simulation. The rest of this paper is organized as follows: Section 2 presents a finite element simulation that demonstrates that the high-frequency vibration isolation performance of the flywheel vibration isolation platform can be affected by the elasticity of its mounting surface. In Section 3, a simplified 2-DOF theoretical model is analyzed to examine the influence of the structural plate stiffness on the overall isolation efficiency of the plate-isolator system. In Section 4, a simplified 3-DOF model is used to verify that applying an elastic boundary to the structural plate can effectively improve the overall isolation efficiency of the plate-isolator system, and the stiffness of the elastic boundary is optimized. Section 5 verifies the theoretical optimization results through finite element simulation, which shows that the overall isolation efficiency of the plate-isolator system will be significantly improved due to the plate's elastic boundary. Finally, in Section 6, the research conclusions are further verified using a cubic satellite structure, and the finite element simulation results show that setting an elastic interface between the plates on which the flywheels are installed and other plates can significantly reduce the vibration response at various positions of the cubic satellite.