In this study, we propose a rectangular and cylindrical three-dimensional space sound absorber using a permeable membrane and the absorption characteristics which are examined experimentally by reverberation room method. As a pilot study, a two-dimensional boundary element (2-D BEM) analysis is also conducted to predict the absorption characteristics of the absorbers. The experimental study revealed that the absorption coefficient is low at low frequencies and gradually increases with frequency. The absorption coefficient converges to 0.5 at the maximum which is similar to a single-leaf permeable membrane. The flow resistance and the surface density of the permeable membrane mainly affect the absorption characteristics at middle to high frequencies. At low frequencies, the heavy membrane contributes to the higher absorption performance. In the experiment specimens with high flow resistance produce higher absorptivity. Also, the cylindrical absorber shows slightly higher absorption coefficient than the rectangular absorber mainly at low frequencies. The 2-D BEM results show similar frequency characteristics as the measured values when the membrane's flow resistance and surface density are low, but the numerical values overestimate overall the absorptivity of the absorbers.