Simulations of atmospheric carbonation of Intermediate-Level Long-lived radioactive Waste (ILLW) concrete packages were conducted to evaluate their possible chemical degradations. Two-phase liquid water-air flow is combined with gas component diffusion processes leading to a progressive drying of the concrete. Complete drying of the 11 cm thick waste disposal package wall occurs over a period ranging from 2 years for the low-performance concrete to 10 years for the high-performance concrete. The drying process slows down when transport characteristics of concretes are enhanced. Carbonation depths in the order of 2 to 3 cm in 100 years are predicted for this cementitious component. However, these values are slightly overestimated compared to experimental data. Also the kinetic model of mineral reactivity requires improvements with respect to the protective effect of secondary carbonates and to thermodynamic data.