Literature devoted to experimental measurements of the elastic properties of the human cortical bone gives us a relatively wide spectrum of values. This proves that the result depends on the bone itself and on the area from where the sample has been taken. Ultrasonic measurement, which is a fine technology, points out complex maps. The reason of this very strong heterogeneity is not completely explained. The present study is based on a numerical model of the human cortical bone, the SiNuPrOs model and aims to suggest an explanation. If one admits that mineral apposition occurs around collagen fibres, the spatial orientation of these fibres would have an important consequence on the elastic properties of the medium. On the basis of homogenisation theory allowing to compute all the components of the elasticity tensor, this study quantifies the main influence of this architectural orientation and its effect on the anisotropy of the cortical bone.