The patterns of variation of the 21 anisotropic elastic constants with direction are presented for all of the symmetry systems that are normally expected to occur in rocks and in the constituent minerals. The exception is the triclinic system for which no elastic constants are available. Variations are shown for rotations about the principal axes by means of polar graphs. These include graphs for all of the n-fold symmetry axes possible for elastic symmetry and thus make it possible to visualize variational patterns for rotations about any n-fold axis. Variations throughout space are shown by means of equal area projections for the only constants that are uniquely defined by a singled closed surface. For those unfamiliar with the compliance and stiffness coefficients, the variations that can be shown by young's modulus, poisson's ratio, and shear modulus are also given. The significance of anisotropy and the necessity of using it to understand and predict behavior of rocks is being given increased recognition. The included visual presentations will greatly aid in understanding anisotropic elasticity and the variation of rock properties with direction.