Seismic isolation is the most effective way to achieve earthquake resistance of equipment located inside buildings and structures. Achievement of seismic stability power plant turbine foundation by applying a variety of design solutions and seismic isolation systems is a significant issue. The Earth population growth and as a result, an increase in the required electric capacities are the main causes to design and build more facilities of increased responsibility (such as power plants) in areas with high-level seismic actions. Improving the reliability and safety in the design of power plants is achieved by the resistance of buildings, structures, and equipment to special types of external influences, including seismic. Ensuring the seismic resistance of building structures and technological equipment is one of the key tasks in the design of power plants in seismically active territories. A new constructive solution of the turbine building is proposed: the turbine building, which contains the turbine unit foundation, which is vibration-insulated with spring and spring-damper blocks, is completely isolated by introducing a layer of seismic isolators under the foundation plate of the building. The turbine unit foundation is twice isolated. Plenty of calculation experiments using the FEM were carried out. Three different structural schemes of the turbine unit foundation as part of the turbine building are analyzed: foundation without seismic isolation; classic vibration-insulated foundation (foundation with a standard seismic isolation system); foundation with double seismic isolation system. The dynamic behavior of the foundation with a double seismic isolation system is also analyzed at a different vertical stiffness ratio and horizontal stiffness ratio of the “bottom” layer seismic isolators. The greatest decrease in horizontal seismic accelerations in the axial direction at the turbine installation level achieves when the double seismic isolation system with slider seismic supports in the lower layer is used.