Up to now, most of the research concerning structural acoustic topology optimization has concentrated on the macro scale, i.e.the macro structural layout or material distribution[1-3].However, if we look into in detail some real acoustic structures or materials used in engineering, a pattern of composites with periodic microstructure can be often found.On the other hand, plenty of work on microstructural design has been carried out for different application area to improve the material properties[45], such as mechanical properties, thermal or thermal-elastic properties, electro-magnetic properties, piezoelectric properties and so on.However, less work concerns acoustic properties.Therefore, it is natural to extend the models for structural acoustic topology optimization to the micro scale, or even an integration of the two scales Topological design of the periodic microstructure with respect to minimization of the total sound power radiation from the boundaries of the macrostructure is studied in the present paper.The macrostructure is excited at a single or a band of excitation frequencies by a time-harmonic external mechanical loading with prescribed amplitude and spatial distribution.The structural damping is considered to be Rayleigh damping.The microstructure composed of two different solid isotropic material phases is assumed to be identical from point to point at the macro level, which implies that the interface between the structure and the acoustic medium will not change during the design process.The upper limit of the volume fraction of the strong material is given in the design.