The article by Ekkart Kröner discusses the calculation of elastic constants for a polycrystalline material from the elastic constants of its single crystals. Using the concept of elastic polarizability, Kröner shows that the shear modulus can be derived from a third-degree equation involving combinations of the single crystal principal elastic constants. The experimental results show some discrepancies with the calculated values, indicating that the experiments did not meet the ideal conditions required by the theory. The method is further discussed for its potential applications. Kröner reviews previous works on the topic, noting that while initial comparisons between theoretical and experimental elastic constants suggest everything is in order, a closer examination reveals that the calculations are often weakly theoretically founded. The uncertainty is increased by the difficulty in selecting the necessary experimental data from a variety of results. The concept of elastic polarizability, introduced by Eshelby, allows for a calculation of the elastic constants of a polycrystalline material on a solid theoretical basis without ad hoc assumptions. The article also provides definitions of key terms and notations used, such as tensor components of stress and strain, Euler angles, and various elastic constants. It highlights the relationship between the four-index and two-index elastic constants in cubic crystals and the fact that a polycrystal composed of cubic crystals has the same compression modulus as a single crystal. Finally, the article reviews previous results, including Voigt's approximation, which assumes all grains undergo the same deformation and does not account for boundary conditions, leading to overestimates of the Young's modulus and shear modulus by up to 20%.The article by Ekkart Kröner discusses the calculation of elastic constants for a polycrystalline material from the elastic constants of its single crystals. Using the concept of elastic polarizability, Kröner shows that the shear modulus can be derived from a third-degree equation involving combinations of the single crystal principal elastic constants. The experimental results show some discrepancies with the calculated values, indicating that the experiments did not meet the ideal conditions required by the theory. The method is further discussed for its potential applications. Kröner reviews previous works on the topic, noting that while initial comparisons between theoretical and experimental elastic constants suggest everything is in order, a closer examination reveals that the calculations are often weakly theoretically founded. The uncertainty is increased by the difficulty in selecting the necessary experimental data from a variety of results. The concept of elastic polarizability, introduced by Eshelby, allows for a calculation of the elastic constants of a polycrystalline material on a solid theoretical basis without ad hoc assumptions. The article also provides definitions of key terms and notations used, such as tensor components of stress and strain, Euler angles, and various elastic constants. It highlights the relationship between the four-index and two-index elastic constants in cubic crystals and the fact that a polycrystal composed of cubic crystals has the same compression modulus as a single crystal. Finally, the article reviews previous results, including Voigt's approximation, which assumes all grains undergo the same deformation and does not account for boundary conditions, leading to overestimates of the Young's modulus and shear modulus by up to 20%.