Durability of concrete exposed to an external sulfate attack is a great concern for long-time reliability of nuclear waste containment. Concrete can be subjected to moderate external sulfate attacks, leading to the precipitation of gypsum and ettringite in the porous media. The formation of these minerals generates internal swelling pressures, leading to cracking and expansion of the material, reducing its containment properties. This paper presents experimental results obtained on cement paste samples subjected to a low concentration (30.10-3 mol/l) external sulfate attack during 6 months in realistic service conditions. Samples were characterized using multiple experimental characterization tools such as XRD, SEM-EDS, and nanoindentation to follow the evolution of chemical, mineralogical, microstructural and mechanical properties of the material. Cement paste samples with different C3A ratios were used to boost either ettringite or gypsum formation during the chemical attack in order to assess the impact of each mineral on the degradation. Results showed apparition of cracks parallel to the attacked surface, located in the gypsum formation and portlandite dissolution area. This observation suggested an active participation of gypsum formation in the expansion mechanism. Numerical simulations of the chemical degradation were performed using the reactive transport code HYTEC in order to enrich the interpretation of experimental results. Based on simulation results, an analytical homogenization scheme was applied to estimate Young Modulus values in the degraded area. Depth values of degradation fronts and calculated elastic properties were in good agreement with experimental results.