Pressure dependence of gas permeation flux for dual-phase ionic-conducting membranes is critical to the design and operation of separation or reaction processes using these membranes. However, literature on dual-phase membranes has mainly focused on temperature, rather than pressure dependence of gas permeation flux. This paper presents a theoretical approach for the development of the pressure dependence of gas permeation flux for dual-phase membranes, demonstrated with CO2 permeation for samarium-doped-ceria (SDC)/molten-carbonate (MC) dual-phase membranes. The paper presents a model showing that gas permeation through dual-phase ionic-conducting membranes is controlled not only by the intrinsic ion (or electronic) conductivity of the materials for each phase, but also by the geometric factor defined as the ratio of the volume to tortuosity of each phase. These geometric factors for both phases are determined by the topological structure of each phase. Dual-phase membranes of the same materials can have very different pressure-dependent flux equations depending on the topological structure dictated by synthesis method and conditions. CO2 permeation through SDC-MC membranes made of SDC with low porosity is controlled by carbonate conduction in the molten carbonate phase, leading to logarithmic CO2 pressure-dependent flux equation. CO2 permeation through SDC-MC membrane of SDC with intermediate porosity is controlled by oxygen ionic conduction in the SDC phase, and the CO2 permeation flux shows power-law dependence on CO2 pressures. The validity of the model is confirmed by comparison of the modeling results with experimental CO2 permeation data for SDC-MC membranes. This work provides a direction for developing pressure-dependent gas permeation flux equations for various dual-phase ionic-conducting membranes.