Data on the elastic properties of single crystals has increased dramatically since Professor Simmons completed his first book in 1965. While this book is a consolidation of his earlier work, it has been extensively updated and revised to include new material and references, is far more complete, and is presented in a more useful form. This is actually a handbook consisting of computer printout in tabular format. It presents data on the elastic properties of single crystals collected from the literature through mid-1970 and the elastic properties of isotropic aggregates which are calculated according to the schemes of Voigt and Reuss for all materials, and Hashin and Shtrikman for materials with cubic symmetry. The tables include about 3000 determinations. At present it is impossible to calculate the elastic properties of a random, macroscopically isotropic aggregate of crystals from the single crystal elastic constants, but bounds may be obtained for the aggregate properties from the single crystal constants. Accordingly the book tabulates the Voigt and Reuss averages for all materials for which single crystal data has been reported. Hashin and Shtrikman have shown that the Voigt and Reuss bounds could be improved, and they have developed expressions for the corresponding bounds of aggregates of cubic crystals. In this book all four bounds (Voigt, Hashin, Shtrikman, and Reuss) are tabulated for cubic materials while Voigt and Reuss bounds only are tabulated for non-cubic materials. The elastic properties of aggregates are those in common use and include Young's modulus, shear modulus, Poisson's ration, bulk modulus, compressibility, velocity of compressional waves, and the velocity of shear waves. Although any two of these properties suffice to uniquely characterize a given material, all are tabulated because different sets are best suited for different uses.