In the last years, transport of gases in clay buffer materials for Engineered Barrier Systems (EBS) has been deeply investigated by many research programs in the framework of nuclear waste storage. At present state, the coupled hydromechanical models to analyse this kind of problems provide qualitatively description of the gas transport phenomena but their predictive capabilities are still limited, indicating that the physical phenomena that rules the gas transport process are not understood in sufficient detail. The gas transport phenomenon is strongly influenced by material heterogeneities and by the hydromechanical coupling of the involved phenomena. From a modelling perspective, the hypothesis of perfect homogeneity of the buffer material is not realistic and leads to important errors in the assessment of material behaviour. In the present contribution, Lagamine has been used as a basic tool of a Stochastic Finite Element Method (SFEM) analysis. It represents a well-known approach to consider the effect of material uncertainties by using a deterministic FEM tool. A series of finite element analyses with increasing degree of complexity have been performed and compared with high-quality laboratory tests performed on compacted bentonite. The influence of the constitutive assumptions and of the material heterogeneity have been analysed in terms of hydration kinetics, swelling behaviour, breakthrough pressure, and kinetics of gas dissipation. The most relevant outcome of the study is the possibility of analyse each step of the finite element modelling to highlight critical points of the simulation process focusing the sources of uncertainty and orienting the subsequent experimental and modelling phases.