In a Deep Geological Repository (DGR) for the long-term containment of radioactive waste, the engineered barriers and host clay rock inhibit the migration of gases, due to their low permeability and high gas entry pressure. Some experiments in the literature have focused on the measurement of gas entry pressure (Pg,e), but there is a lack of 2-phase flow (water-gas) modeling studies that include entry pressure effects in such porous media. In the present work, the modified Van Genuchten-Mualem model (Vogel et al. 2001) is extended to two-phase flow, incorporating the capillary entry pressure parameter (Pc,e), and a new data analysis approach is developed in order to characterize the water-gas constitutive relations (saturation curve, water permeability curve, gas permeability curve). This constitutive model is then implemented in the iTOUGH2 code [46] with a change of primary variables to be described below (capillary pressure is set as primary state variable instead of gas saturation). After regression tests for verifying the change of primary variables in iTOUGH2, two problems were modeled: first, numerical flow experiments were performed in a clay soil (code-to-code benchmark tests, and comparisons focused on entry pressure effects); secondly, water-gas migration was modeled based on an in-situ gas injection experiment (PGZ1) performed in the French URL (Underground Research Laboratory) of Bure. Sensitivity analyses show that gas entry pressure is an important controlling factor which should not be neglected in simulations of gas migration in clayey materials.