A methodology, based on synchrotron X-ray nano-tomography measurements, is proposed to obtain 3D reconstructions of porous supports for Solid Oxide Fuel Cell (SOFC). The methodology has been applied to investigate the microstructure of a typical Ni-8YSZ cermet substrate of an Anode Supported Cell (ASC). Experimental conditions have been optimised so that a 3D reconstruction of 42 μm × 42 μm × 105 μm has been computed with a voxel size of 60 nm. The 3D reconstruction has been numerically analysed showing a quasi isotropy over the medium. A special attention has been paid to compute the morphological properties controlling the gas diffusion through the support. In this frame, it has been found that a volume as large as 35 μm × 35 μm × 35 μm is required to be statistically representative for the whole substrate. More particularly, the tortuosity factor τ has been calculated on the basis of finite element simulations. The effect of the boundary conditions taken for these simulations has been investigated. In the direction perpendicular to the anode/electrolyte interface, the tortuosity factor has been determined to tau(z) = 2.8(-0.2)(+0.3).