The physical properties of fibrous materials are closely linked to their microstructure. In order to characterize their microstructures as effectively as possible, all fibres in a sample should be individualized. This work mainly aims at developing a new fibre analysis method that segments a 3D greyscale tomography image into a background and a set of connected components, each representing a single fibre. Properly completed fibre analyses may provide input data for generative or synthetic models, which can in turn be used to estimate various characteristics of the material. In this paper, we introduce an original method based on the skeletonization of the fibre mass, followed by a geometrical analysis of the obtained skeleton. Based on this procedure, several measurements can be computed (e.g. length, orientation, number of contacts). Furthermore, we validate the reliability of our fibre analysis process using various comparisons between our results and artificial ground-truth data.