Abstract In a deep geological repository (DGR) for the long-term containment of radioactive waste, gases could be generated through a number of processes. If gas production exceeds the containment capacity of the engineered barriers or host rock, these gases could migrate through these barriers and potentially expose people and the environment to radioactivity. Expansive soils, such as bentonite-based materials, are currently the preferred choice of seal materials. Understanding the long-term performance of these seals as barriers against gas migration is an important component in the design and long-term safety assessment of a DGR. This study proposes a hydro-mechanical linear poro-elastic visco-capillary mathematical model for advective-diffusive controlled two-phase flow through a low-permeability expansive soil. It is based on the theoretical framework of poromechanics, incorporates Darcy’s Law for both the porewater and poregas, and a modified Bishop’s effective stress principle. Using the finite element method (FEM), the model was used to numerically simulate 1D flow through a low-permeability expansive soil. The results were verified against experimental results found in the current literature. Parametric studies were performed to determine the influence on the flow behaviour. Based on the results, the mathematical model looks promising and will be improved to model flow through preferential pathways.