In low/intermediate-level waste (L/ILW) repositories, anaerobic corrosion of metals and degradation of organic materials produce mainly hydrogen, methane, and carbon dioxide. The Swiss reference concept for the L/ILW repository consists of parallel caverns sealed off from a single access tunnel in a deep low-permeability claystone formation. The potential buildup of excess gas pressures in the backfilled emplacement caverns was investigated in a series of two-phase flow models. In the first step, a large-scale model was constructed, implementing the 3D radial tunnel and cavern geometry with a simplified rectangular geometry. In the second step, the potential impact of the detailed geometry of the engineered barrier system (EBS) and the associated heterogeneity inside the cavern was examined using detailed models of the repository caverns, tunnel seals, access tunnel, and surrounding host rock. The simulation results from the large-scale 3D repository model show that during the early post-closure period simulated pressures can vary significantly between different parts of the repository. The simulated pressure increase in the emplacement caverns remained below the fracture pressure of the rock for realistic assumptions. Gas flow is largely limited to the EBS and the excavation disturbed zone (EDZ); thus, gas flows through and around the repository seal into the adjacent tunnel system, which is also demonstrated in the detailed repository-cavern model. The repository seal model described the detailed two-phase flow pattern of early time resaturation of the repository by water inflow from the ramp and subsequent counter flow associated with the gas flow from the repository cavern. Overall, the results of the detailed models complement and confirmed the results of the large-scale 3D model in terms of the timing of the pressure peaks and the migration of gas from the cavern into the surrounding host rock and through the repository seal.