Metamaterial surfaces can be conceptualized by 2-dimensional periodic arrangement of many small flat inclusions on an otherwise homogeneous host surface. Electromagnetic properties of such metamaterial plates, which can indeed be regarded as frequency-selective surfaces, are influenced by the shape and geometry of these inclusions. When a metamaterial surface is closely placed above a perfectly conducting plate, at certain band of frequency, this structure may possess high surface impedance at its top surface, and thus providing a high-impedance ground plane (HIGP). The center frequency and bandwidth over which such high-impedance electromagnetic surface is achieved depend on inclusion shapes and compositions, among other parameters. By placing a resistive sheet on top of this surface, we can achieve a thin structure that can be an efficient absorber for incident electromagnetic energy.