Corrosion of steel canisters disposed of in a geological repository for high-level waste leads to generation and accumulation of hydrogen gas which may significantly affect long-term safety of the repository. Numerical modelling can be used to predict the likely hydraulic evolution of such a disposal facility and to estimate the influence of generated gas on repository safety.This article presents a two-phase flow (not taking into account mechanical coupling) gas migration model developed in the original version of the computer code TOUGH2-MP (USA). An important and new aspect of this model is its capability to introduce a network of very thin interfaces in three-dimensional analysis of gas migration. This model was verified in the international benchmark exercises in the recent European Commission project FORGE (Fate Of Repository GasEs). The analysis was focused on the results of a second benchmark exercise, i.e. hydrogen gas behaviour in a part of a geological repository (module) situated in clay formation, and sensitivity analysis. The results showed that the interfaces, backfill and excavation disturbed zone are the main migration and accumulation media for gaseous hydrogen in the repository module. The peak pressure in the module did not exceed the geological environment pressure at a depth of 500m, and is not sufficient to disturb mechanical stability and functionality of the system of engineered and natural barriers.