Recently, more or more interests have been cast into the periodic composites media such as periodic chiral materials, periodic negative materials and frequency selective surface and the like. In general, these periodic structures are constructed by periodically embedding planar or non-planar metal objects into a host dielectric with lossy or lossless. Electromagnetic analysis of the periodic structures by integral equation methods has been conventionally conducted in the spectral domain. Though spectral analysis is generally less suited than the spatial analysis to the shape of structures, it has traditionally been preferred since the involved Green’s functions are easily derived and evaluated. While their spatial domain counterparts have required computationally expensive numerical operations. More recently, however, techniques based on complex image theory have been developed to efficiently evaluate the spatial domain Green’s functions. In this regard, spatial and spectral approaches are now placed on an equal footing. This research involves numerical techniques well served by this development, including the high frequency structures, which are non-periodic, and the composite media, which are periodic.In the solution of the above structures, the moment of method is employed to discretize the integral equations for finding the surface charges and currents on the unit periodic element, which can be arbitrary shape. In this research, the periodic structures to be modeled included finite array and infinite array sandwiched into multilayered dielectric slab or suspended in free space. Fast full wave analysis of these structures needs efficiently calculation of the Green’s functions. For finite array, the Green’s functions are rapidly computed by using complex image theory combined with matrix-of-functions techniques or Prony’s method. A numerically efficient scheme has been presented 1:0 obtain the spatial Green’s functions for the multilayered structures. For infinite array, the Ewald’s method and Shank’s transformation are used to fast sum of the periodic Green’s functions in spatial and spectral domain.In solving the resultant matrix equations, the iterative methods combined with accelerating techniques such as Fast Fourier Transformation (FFT) are also applied. Their application to an array of arbitrary shape elements has been covered and studied. Finally, a highly efficient numerical technique based on the hybrid spatal-spectral domain and CG-FFT has been developed. Some structures for instance periodic chiral materials, frequency selective surface are simulated. The characters of reflection and transmission or Radar Cross Section (RCS) are solved.