На підставі аналізу сучасного стану проблеми аеропружності турбомашин і існуючих методів прогнозування флатера можна зробити висновок, що найбільш перспективним підходом у дослідженні аеропружної поведінки лопаткового вінця турбомашини є підхід, заснований на тривимірній моделі нестаціонарної аеродинаміки та модальному аналізі руху лопатки (метод вирішення зв’язаної аеропружної задачі). Цей метод рішення зв'язаної задачі нестаціонарної аеродинаміки та пружних коливань лопаток дозволяє прогнозувати амплітудно-частотний спектр коливань лопаток в тривимірному потоці газу, включаючи вимушені коливання, самозбудні коливання з метою підвищення надійності лопаткових апаратів турбомашин. The aeroelasticity of the cascades of blades is considered to be the most burning and important problem, because it effects the reliability of the flow channels of turbine machines. The main complexity of the investigation of aeroelastic phenomena that occur in turbine machines consists in the need of the simulation of the interaction of the two physical environments (liquid and elastic). One of the approaches to the computation of aeroelastic phenomena (the flutter) is the nonstationary aerodynamic analysis that studies nonstationary flows in turbine machines independently of their origin and over the past decades it covered the way from the linear theory to the solution of Navier -Stokes equations. The second approach to the investigation of the aeroelasticity of the cascades of blades of turbine machines is related to the studies of the motion of blades under the action of aerodynamic forces induced by the nonuniformity of the main flow and independent of the motion of the blades. These approaches ignore the influence of vibrating blades on the main gas flow. Within the framework of individual problems considered in scientific papers the problem of self-excited vibrations (the flutter) that are the most complicated and least studied phenomena falls out of consideration. Based on the analysis of the contemporary state of the problem dealing with the turbine machine aeroelasticity and available methods of the flutter prediction we can draw a conclusion that the most promising approach to the investigation of the aeroelastic behavior of the blade row of the turbine machine is the approach that is based on the three-dimensional model of the nonstationary dynamics and the modal analysis of the blade motion ( the method of the solution of the coupled aeroelastic problem). This method of the solution of the coupled problem of the nonstationary aerodynamics and elastic vibrations of the blades will enable the prediction of the amplitude-&-frequency spectrum of blade vibrations in the three-dimensional gas flow, including forced self-excited vibrations in order to increase the reliability of the cascades of blades of turbine machines. Using the developed numerical method, we analyzed the aeroelastic behavior of the fan row of the aircraft engine in different modes. The computation data confirmed the appearance of nonstationary modes in the fan operation. The research done allows us to give recommendations on the elimination of the aeroelastic phenomena, i.e. the flutter (by changing the fan blade geometry).