The Task 7 of the EBS task force is devoted to the modelling of gas transport phenomena in saturated bentonite. It was launched mid‐2016 with the following objectives: - To survey existing modelling tools for the simulation of gas migration in saturated bentonite and to compare in a traceable manner the associated constitutive frameworks, required input parameters, capabilities and limitations of the codes in applications related to the gas release from deep geological repositories. - To compare the different modelling approaches in a series of well‐defined benchmark exercises, giving emphasis to the hydromechanical process along the different hydraulic and gas injection/dissipation stages. - To complement existing capabilities of the modelling tools. This includes advanced functional relationships for water retention behaviour and relative permeability, features to mimic colloidal transport and the integration of subscale information from microstructural investigations. In the first phase of the task, the general approach to the problem was defined. In particular, the task specification, the experimental data base on the hydromechanical (HM) behaviour of granular MX‐80 bentonite, and the definition of the model verification and validation procedures were addressed. The second phase of Task 7 concerns the numerical modelling of some specific tests performed on compacted and saturated granular bentonite to assess the capability of the existing HM models to describe the physical phenomena involved in the gas migration process. The material under investigation is National Standard WP2 granular Na‐bentonite from Wyoming (USA). The target of the modelling activity is a set of gas injection tests performed in oedometric conditions on statically compacted and saturated samples (Romero and Gonzalez‐Blanco, 2017). This experimental program involves the microstructural characterization of the granular bentonite (Mercury Intrusion Porosimetry and X‐ray Computed Tomography), the preparation of saturated bentonite specimens, and the execution of gas injection tests in oedometric conditions. In the last year, new elaborations on the material microstructural characterization have been added to the task documentation (Keller, 2018). The proposed modelling approach is based on the Finite Element Code Lagamine (Charlier 1987; Charlier et al., 2001). The code can address multi‐physical problems (THMC) including different nonlinear constitutive approaches and advanced features dedicated to geomechanical problems. The detailed description of the numerical approach to the two phase flow modelling can be found in Dieudonné et al. (2017b). The modelling activity is based on a detailed analysis of the microstructure of the analysed granular bentonite to define its water retention behaviour and to calibrate the hydraulic and mechanical constitutive models (Madaschi & Laloui, 2018). This progress report focuses on the development of a rigorous procedure to estimate the uncertainty of the modelling process. A Bayesian inference approach, the Maximum A Posteriori estimation, was adopted with the aim of estimating the modelling uncertainty including the a priori information derived from the complementary experimental data set. The next stages of the work will be the upgrade of the modelling approach to improve the model performance to reduce the relative uncertainty. The first improvements will be the adoption of an advanced non‐linear mechanical model and the evaluation of the possible source of heterogeneity on the bases of the new microstructural characterization.