MR diffusion-weighted imaging (DWI) uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive a number of parameters that reflect the translational mobility of the water molecules in tissues. In highly organized but asymmetric structures, this mobility may be affected by the obstacles present and this in a direction-dependent way. Important examples of this are white brain matter and the stem of certain plants, both containing fibrous components where diffusion of water molecules across fibers is much more restricted than along the fibers. Diffusion that exhibits such directional dependence is said to be anisotropic, and diffusion tensor magnetic resonance imaging allows localized characterization of this behavior. Interpretation of the information obtained in terms of the underlying tissue structure is often hampered by the complexity of factors that can produce the observed behavior. A phantom that exhibits well-defined anisotropic diffusion and yields sufficient signal can help the experimental testing of the relevant methods and models. In this paper, we have used a phantom consisting of asparagus stems as a test object for assessing the value of the acquisition and postprocessing techniques commonly used in the clinic for this kind of investigation. Because of its strongly fibrous and cylindrically symmetric morphology, exhibiting a well-defined sub-classification of cells on the basis of size and shape, asparagus allows a relatively simple interpretation of the results obtained in the diffusion experiments. Our experiments show that the known structural information about the main cell types encountered correlates well with the behavior patterns of the diffusion parameters.