Anisotropy of the physical properties of rocks is directly related to their internal structure, which is often exhibited by lineation and foliation fabrics as anisotropy markers. Conventional methods of diffraction measurements only provide a part of the structural information that is related to the crystallographic preferred orientation of minerals. In this work, we show the contribution of imaging methods such as X-ray and neutron tomography in studying rock structure that exhibits anisotropic character through lineation and foliation fabrics. In our tomography studies, spherical samples of two different biotite gneisses were tested. Virtual 3D structure models of samples were obtained by both neutron and X-ray tomography, which depict the spatial distribution of mica minerals (biotite and muscovite) - the major carriers of rock anisotropy in the studied samples. An application of scanning method to the 3D data of mica's spatial distribution allowed us to reveal the presence, orientation and strength of foliation and lineation fabrics. We have also performed grain shape analysis using the approximation of the individual elements of segmented mica phase by the equivalent (Legendre's) ellipsoids. As a result, we determined the shape preferred orientations of mica grains and calculated corresponding shape orientation distribution functions. The comparison of structural properties obtained from tomography studies with experimentally determined P-wave, and magnetic anisotropy demonstrated their mutual correlation, providing a basis for the quantitative interpretation of anisotropic rock fabric in relation to the physical properties of rock. The effective elastic and magnetic properties were calculated based on the shape orientation distribution functions determined from tomography data. The good agreement between calculated and measured effective properties have shown the potential of X-ray and neutron tomography for the prediction of magnetic and seismic anisotropy using a 3D model of a rock sample.