Transport of permeates through copolymer membranes with rigid and flexible block was investigated based on the percolation concept. In terms of the morphology, the percolation approach provided a rationale for the property of gas permeation behavior of block copolymer consisting of the rigid amideimide block and the flexible siloxane block. The permeability of oxygen through poly(amideimide)siloxane (SPAI) membranes containing different siloxane contents showed a peculiar permeation behavior, indicating that there existed a percolation threshold of the gas permeation at around 0.2-0.3 volume fraction of SPAI. At above the threshold volume fraction, the gas permeability of this block copolymer was proportional to the probability of spanning siloxane phase. We confirmed that an addition of flexible domains in the rigid matrix enhanced the rate of gas permeation, and the permeability of SPAI obeyed a simple power law above and near the percolation threshold. In order to inspect the present system, the percolation concept was reinterpreted to elucidate the change of gas permeability through polymeric membranes with rigid and flexible block.