Hu, Y. and McMechan, G.A., 2010. Theoretical elastic tensor models at high crack density. Journal of Seismic Exploration, 19: 43-68. Elastic stiffness tensor values in cracked rocks depend on the crack density, and on the shapes, fluid content, orientation, and spatial distribution of the cracks. The mathematical expression of anisotropy is embedded in the elastic stiffness tensor. Thus, in reservoir characterization by anisotropic seismic modeling, inversion and interpretation, a key step is to represent the rock properties in terms of the equivalent anisotropic elastic stiffness tensor. We compare the strengths, limitations, and relationships between the anisotropic elastic stiffness tensor elements predicted for a transversely isotropic medium with a horizontal symmetry axis,using a variety of theoretical formulations, including equivalent single inclusion approximations, smoothing, self consistent approximation (SCA), differential effective medium (DEM) methods, linear slip (LS), and T-matrix methods. These formulations differ in their crack parametrizations, the assumptions and approximations involved, and the corresponding consequences of these. All the formulations involve theoretical extrapolations. Absolute accuracy is not known for high crack density because, while there is substantial internal consistency between the theoretical results when crack interactions are included, there is to date, only limited external validation in terms of physical and numerical experiments at high crack densities. At high crack densities, where crack interactions are important, physically reasonable values are expected to be predicted only by the formulations that implicitly or explicitly consider these effects. These methods are the SCA, DEM, LS and T-matrix methods. For a coal example, all these four methods predict similar elastic stiffness tensor values up to volume crack densities of <0.3, beyond which, the spatial distribution of cracks in the various models becomes increasingly important. In a medium with perfectly aligned fractures, the shear modulus normal to the symmetry plane shows the greatest relative variation between models at high crack density.