The paper describes a cause of the geometric accuracy degradation of slender metallic products during their operation, which consists in the relaxation of residual stresses accumulated while product manufacturing. The most promising technology among the existing technologies of residual stress relaxation is based on the use of vibromechanical vibrations. This technology has high performance and low energy consumption. The reason for the relaxation of residual stresses under the action of vibromechanical vibrations is the gradual accumulation of internal energy, which leads to plastic dislocation shifts upon reaching a critical level. The dislocation motion under the action of vibromechanical vibrations continues until the dislocations take a more compact layout that corresponds to the equilibrium energy state. For technological implementation of the process there was developed a method of ultrasonic stabilization of elastic plates, which serve as sensing elements in differential-pressure transducers. The experimental studies of ultrasonic stabilization are carried out. According to the results of the studies, there have been conducted tests of the microstructure of the control samples. It is established that the samples of steel 20CH13 subject to ultrasonic treatment have a more uniform structure than the samples after the factory technology of long "aging". This confirms the assumption about the structural-energy processes occurring during vibromechanical relaxation of residual stresses. The technology of ultrasonic stabilization can be recommended as a replacement to the "aging" technology on the basis of the obtained results.