Anisotropy in clay-rich sedimentary rocks is receiving increasing attention. Seismic anisotropy is essential in the prospecting for petroleum deposits. Anisotropy of diffusion has become relevant for environmental contaminants, including nuclear waste. In both cases, the orientation of component minerals is a critical ingredient and, largely because of small grain size and poor crystallinity, the orientation distribution of clay minerals has been difficult to quantify. A method is demonstrated that relies on hard synchrotron X-rays to obtain diffraction images of shales and applies the crystallographic Rietveld method to deconvolute the images and extract quantitative information about phase fractions and preferred orientation that can then be used to model macroscopic physical properties. The method is applied to shales from European studies which investigate the suitability of shales as potential nuclear waste repositories (Meuse/Haute-Marne Underground Research Laboratory near Bure, France, and Benken borehole and Mont Terri Rock Laboratory, Switzerland). A Callovo-Oxfordian shale from Meuse/Haute-Marne shows a relatively weak alignment of clay minerals and a random distribution for calcite. Opalinus shales from Benken and Mont Terri show strong alignment of illite-smectite, kaolinite, chlorite, and calcite. This intrinsic contribution to anisotropy is consistent with macroscopic physical properties where anisotropy is caused both by the orientation distribution of crystallites and high-aspect-ratio pores. Polycrystal elastic properties are obtained by averaging single crystal properties over the orientation distribution and polyphase properties by averaging over all phases. From elastic properties we obtain anisotropies for p waves ranging from 7 to 22%.