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Although it is well known that sedimentary rocks can be seismically anisotropic, there have been few detailed investigations of the underlying cause of such anisotropy. Here, we investigate anisotropy due to the preferred orientation of minerals, or lattice preferred orientation (LPO), in a suite of sedimentary rocks. Seismic properties are predicted by averaging single-crystal elastic constants of minerals according to their crystal orientation and modal volume fraction in the rock aggregate. Both Electron Backscattered Diffraction (EBSD) and X-ray Texture Goniometry (XTG) are tested as quantitative techniques for measuring the LPO of sedimentary rocks. Although EBSD has promise for future LPO measurements in polymineralic sedimentary rocks, problems currently remain in measuring low-symmetry phases (e.g. feldspars) and very small clay or mica particles. However, the LPO of very fine-grained phyllosilicates can be measured using XTG and the LPO of low-symmetry minerals can be measured using manual EBSD pattern analysis. Here, we use such a hybrid approach to estimate LPO in a suite of sedimentary samples. The seismic properties calculated from LPO data show anisotropy values for P-waves ranging from 1.5 per cent in sandstones, to over 3.5 per cent in a siltstone, to 12 per cent in a shale. The effect of thin multilayering on long-wavelength propagation in a siltstone is predicted by applying Backus-type averaging. The layering does not enhance the anisotropy because of the small differences in density and in elasticity between the two layer types. The LPO of phyllosilicates and to a lesser extent dolomite and siderite seem to contribute significantly to the seismic anisotropy of phyllosilicate-rich rocks (siltstones and shales). The weak LPO of quartz in sandstones causes a few per cent anisotropy. Cumulatively, our results suggest that field observations of seismic anisotropy have the potential to be used as an indicator of rock lithology. [ABSTRACT FROM AUTHOR]