In the MS group, we implement a number of specific tests to observe both the deformation and the fatigue life of a structure subjected to a non-linear mechanical loading under vibration environment. The goal is to determine a criterion of crack initiation with vibration fatigue. It is better to take into account the nonlinearities of behavior in the formulation and the ingredients of the criterion. Our idea is to consider the fatigue criterion with the base of the eigenmodes of the structures. The difficulty lies in the calculation of the modal basis in the case of the structures under stress at high temperature in the viscoplastic regime. From an industrial point of view, the main goal is better understanding of the phenomena of vibration fatigue at high temperatures. This is for a method of calculating resonance mode in the presence of material nonlinearity and sketch a method of fatigue design for such structures.