Gas turbine blades operate in a wide frequency range of dynamic loads. Such loads can lead to fatigue deformations and microcracks with time, which changes the dynamic characteristics of the  of the blades. The blade is an elastic structure and has a spectrum of natural frequencies and vibration modes. They affect the dynamic properties of the blade itself and its ability to respond to various influences. The study consists in studying the natural frequency and vibration modes of turbomachine blades and in improving the methods of numerical prediction of dynamic response of blades under load, which is an urgent task, as it allows to characterize the dependence of natural frequencies of vibrations on the mode of operation and reliably avoid resonance for engineered blades in actual operating conditions.