The rotor blades of the last stages of steam turbines have a considerable length and weight, and are subjected to significant unsteady loads, so the problem of the appearance of self-excited oscillations or auto-oscillations is relevant. Such oscillations are quite dangerous, reduce the blade system's service life, and affect the flow characteristics in the turbine. During the operation of a 370 MW steam turbine, damage was detected in the last stage rotor blades in the root region. Numerical studies did not reveal the conditions for the occurrence of oscillations with a dangerous amplitude. In this regard, a numerical analysis of the aeroelasticity of the last stage rotor blades was performed using an improved numerical method for modeling unsteady aerodynamics and harmonic oscillations of the blades. The results of the numerical study are presented in the form of a distribution of the work of aerodynamic forces on blade displacement for different values of interblade phase angles, as well as by blade height for the first five natural oscillation modes. The results of the calculations showed the presence of conditions for the excitation of blade oscillations for the first natural mode in one of the steam turbine operating modes.