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 mu m x 42 mu m x 105 mu m 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 mu m x 35 mu m x 35 mu m is required to be statistically representative for the whole substrate. More particularly, the tortuosity factor tau 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). (C) 2011 Elsevier B.V. All rights reserved.