In this paper, periodic and hybrid trichiral structure is developed as the raft in a floating raft system to enhance isolation performance in the medium and high-frequency range. Firstly, wave propagation in the periodic trichiral structure is analyzed through Bloch theorem. Further study of the hybrid trichiral structure, consisting of multilayer of cells with different geometry, demonstrates that the stop band of this assembly is the superposition of the band gap generated by individual cells. This feature can be used to extend the stop band without affecting the performance in other frequencies. Vibration transmission of the floating raft system is studied through frequency response function based substructuring method. Numerical examples indicate that the sound power radiated from the foundation can be greatly attenuated in the stop band of the periodic trichiral raft. Based on the feature of hybrid structure, an optimization scheme with respect to the trichiral raft is developed with the aim of minimizing the radiated sound power of the system. The proposed modeling and optimization method can be extended to design other regular raft structures with great flexibility.