For the first time, we determine the modulus of elasticity (Young's modulus), the shear modulus, and the coefficient of transverse deformation (Poisson's ratio) for hot-pressed dodecaborides by using the basic thermal characteristics of the dodecaborides of rare-earth metals and zirconium YB and the experimental methods of static and dynamic investigations. The numerical and experimental values of the mechanical parameters coincide. The modulus of elasticity of dodecaborides is approximately twice smaller than for pure boron and does not increase, as theoretically predicted, in the sequence MeB 4 → MeB 6 → MeB 12 . This fact can be explained by the structural features of the crystal lattice of dodecaboride phases, the lengths of the B-B, Me-B, and Me-Me bonds, and the forces of interaction between the atoms in these phases.In the contemporary branches of industry (chemistry, metallurgy, machine building, radio electronics, aircraft and spacecraft construction, nuclear and defense technologies), traditional metals and their numerous alloys fail to satisfy new requirements to the chemical stability, density, and physicomechanical properties, especially under the conditions of high mechanical loads, high temperatures, and the action of corrosive media. The scientific progress, as well as the economic and ecological requirements determine, to a significant extent, the properties of structural materials used in manufacturing various types of commercial products. The problem of creation of new classes of structural materials based of rare-earth metals (REM), carbon, silicon, boron, and other elements in the form of carbides, silicides, borides, and compositions of these compounds explains the necessity of profound scientific investigations of the physicochemical and mechanical properties of these materials. It is clear that the dodecaboride phases of REM and zirconium with structures of the UB 12 type definitely belong to the indicated class of materials.The physicochemical properties of these refractory compounds and, especially, their mechanical and strength characteristics are studied insufficiently [1][2][3][4]. Here, it is necessary to mention only the paper [5] in which it is shown that the bending strength of YB 12 is equal to 165 GPа (and the porosity of the specimens sintered in vacuum is 22-26%). In addition, in [2], one can find the computed values of Young's modulus for the dodecaborides of REM.The aim of the present work is to study the principal mechanical properties of cubic dodecaborides with the UB 12 structure, namely, to perform the numerical analysis (by using the well-known formulas) of Young's and