Acoustical porous materials containing specific porous inclusions are studied. An extension of double porosity model based on the homogenization hypotheses introduced by Boutin [1] is presented. To apply and extend Olny's model [2, 3], some hypotheses together with the identification of the different regimes rely directly on the nature of the inclusion must be respected that is why the filling material is chosen to respect those assumptions (for example high contrast of permeability,. . . ). The inclusions are supposed periodic and the frame rigid. The idea here is to use the diffusion effect already observed in double porosity case and to add poro-elastic inclusions to deal with the main disadvantage of double porosity case, i.e the presence of an hole. This hole leads to bad absorption bahavior at very low frequency and loss of performances in transmission. Experimental verifications are given by using different Kundt tubes. The semi-phenomenological model is thus validated.