[en] The main objective of this report is to establish the analysis and evaluation methodology of the progressive thermal buckling behavior for the LMR structures subjected to moving high temperature cycles. To do this, the ANSYS version 7.1 was used with the nonlinear material constitutive equation of Chaboche's model. Using this model, the progressive thermal buckling behavior was identified for the cylindrical structures having the free edge. As an example of the application, the progressive thermal buckling analysis for the KALIMER was carried out, and the results are described in this report