The aim of this work is to study the structure of three-dimensional and two-dimensional loose packing of stiff cylindrical fibres, with a particular attention for the 2D structures, according to their aspect ratio. First, we have carried out an experimental study of the porosity for 3D and 2D packing. In this last case, the Elementary Representative Surfaces have been determined. Then, an attempt of interpretation of the porosity variations for 2D stacks has been realized on the basis of the Excluded Volume theory and a variation law has been proposed. We have also studied the relevance of a simplified packing model based on a single geometry of the defects. Then, some local properties of 2D stacks such as the densities and the sizes of the defects or the orientations of the fibres have been determined.