Elastic anisotropy of sheet-silicate-rich rocks such as shalesand slates strongly depends on the orientation distribution ofplatelet-shaped minerals, as well as shape and orientation ofpores. Bulk elastic anisotropy of the rock results in the anisotropywith respect to the propagation of elastic waves, and consequently,the fastest P-waves can travel with velocities exceedingthe slowest velocities by a factor of two or even greater. An importantfactor is the sheet-silicate's grain shapes.We approacheda model system of biotite platelets in an isotropic matrix withdifferent methods: A mean-field self-consistent method thatconsidered ellipsoidal particles in an effective anisotropic matrix,and a full-field method based on fast Fourier transformsthat considered the microstructure, the topology of the polycrystal,and local interactions. Both methods provided numericallyvery close results. Using these results, we predicted that the aggregatewith more oblate grain shape (thinner platelets) waselastically more anisotropic than the material with grains of lessoblate shape, but only for small volume fractions of orientedplatelets. For large fractions of platelets, the opposite was true.This switchover in the elastic anisotropy depended on texturestrength, platelet shape, and elastic properties of the isotropicmatrix.