Diffusion weighted magnetic resonance imaging offers a non-invasive tool to explore the three-dimensional structure of brain white matter in clinical practice. Anisotropic diffusion hardware phantoms are useful for the quantitative validation of this technique. This study provides guidelines on how to manufacture anisotropic fibre phantoms in a reproducible way and which fibre material to choose to obtain a good quality of the diffusion weighted images. Several fibre materials are compared regarding their effect on the diffusion MR measurements of the water molecules inside the phantoms. The diffusion anisotropy influencing material properties are the fibre density and diameter, while the fibre surface relaxivity and magnetic susceptibility determine the signal-to-noise ratio. The effect on the T2-relaxation time of water in the phantoms has been modelled and the diffusion behaviour inside the fibre phantoms has been quantitatively evaluated using Monte Carlo random walk simulations.