Acoustic meta-materials are widely known with their extra-ordinary sound properties like transmission, absorption and orientation which are not available in natural materials. These features are provided by their repeating constructions and various configurations. Sound absorbers are used in a wide variety of applications such as sound treatment in buildings, vehicles, concert halls and any place noise control and/or desirable acoustic properties are required. Traditional sound absorbers are long-known to be inefficient in the low frequency ranges. In this study, to overcome the absorption problem in low frequencies, absorption characteristics of foam based porous structures are analyzed with the addition of locally resonant blocks. Elements embedded in the absorber material with various shapes and properties are investigated by finite elements method to improve sound absorption, especially in the low frequency range. The results showed that embedding air cavities enclosed by thin solid shells to the absorber improves sound absorption in the low frequencies without significant deterioration in the high frequencies.