A technique for determining the mechanical characteristics of nanoobjects is presented. A heterogeneous material consisting of a nanophase and a binder phase with specific mass and volume concentrations is considered. A heterogeneous material is reduced to homogeneous by the averaging methods, and the mechanical characteristics are associated with the averaged characteristics. Assuming that the mechanical characteristics of the binder and averaged homogeneous materials are known from experimental data, the system of equations is obtained that allows us to determine the mechanical characteristics of nanoobjects included in this heterogeneous material. Classical experiments were carried out describing the uniaxial stress and strain state of materials to establish the analytical dependences of the mechanical characteristics of nanophases on their size. Specific examples are given for silicon dioxide nanoparticles (Aerosil and Tarkosil powders).