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, the 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 mathematical hydro-mechanical (HM) model for migration of gas (two-phase flow) through a low-permeable heterogeneous swelling geomaterial. It is based on the theoretical framework of poromechanics, applies Darcy's Law for both the porewater and poregas, and incorporates a modified Bishop's effective stress principle. The study expands upon previous work by the authors, by assessing three stress-strain constitutive models in an attempt to simulate dilatancy-controlled gas flow; i) an enhanced elastic damage model, ii) an elastoplastic model with damage, and iii) a non-local elastoplastic model with damage. Using the Finite Element Method (FEM), the models were used to simulate axial and radial flow through a low-permeable swelling soil. The results were validated against experimental results found in the current literature for a confined cylindrical sample of near-saturated bentonite under a constant volume condition. This study provides insight into the use of highly coupled HM models, their influence on the stress state of the material, and their capabilities to represent multi-phase flow in a swelling geomaterial.