Creation of the new generation of power equipment (nuclear reactors, gas turbine plants, special power plants) with increased operational parameters and meeting high safety requirements, entails the goal of creating novel domestic methods for determining stresses and strains that occur in the most critical elements during operation of such installations. The new approaches, including the restoration and development of domestic competencies in the creation of means for experimental control of deformations in elements of the equipment at high temperatures are proposed. The results of developing indirect methods providing determination of the deformations at the most critical points of the structure based on solutions of the inverse problems of experimental mechanics are presented. Improved algorithms for processing experimental information and determining strains from measured stresses are considered for the case of inelastic behavior of the structural material in the zones of tensometric measurements. The improved hermetic strain gauges resistant to lead and sodium coolant are proposed for experimental determination of the deformations that occur on the internal surfaces of the liquid metal coolant circulation circuit of new nuclear reactors of BN and BREST types. The results of tests of the developed measuring instruments in liquid sodium medium at a temperature of 540°C during bench tests are presented. In conditions of increased requirements for assessing the effect of the strain gauge creep on the measurement results obtained at high temperatures, a stand design has been developed that makes it possible to determine the boundaries of a possible error at temperatures up to 600°C under dynamic loading of the structure. To determine the stresses arising at dangerous points of the heat exchange equipment of BN type reactors located in inaccessible areas of the inner surface of the facility, an iterative algorithm for solving the inverse problem of thermoelasticity is proposed, using the measured values of stresses and temperatures on the outer surface of the structure. A set of improvements to the traditional method of full-scale tensometric study is proposed proceeding from of the analysis and implementation of the data obtained.