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In the paper the research methods of axially symmetric elastic - plastic stress strain state of structures in the form of thin single and multiple layer shells of rotation with an account of material damage at creep is represented. The long-term strength criterion definition, on the basis of which the time to failure of the structure is calculated, is one of the important task. There are multiple long-term strength criteria, but very little detail recommendations on their usage and concretizing, which is what makes this problem so difficult to solve. The authors proposed a simple and easy-to-use method for concretizing the Pisarenko–Lebedev generalized long-term strength criterion. To verify the reliability of the proposed method of concretizing the long-term strength criterion, the calculations of time to failure a cylindrical shell under the action of internal pressure and a thin lamina with a round hole stretched by external radial forces are carried out. The calculation results obtained by the proposed method differ from the experimental ones by 1.8% and 3.1%. These results are the most reliable. Therefore, proposed method for calculating the long-term strength criterion enables more accurate damage and time-to-rupture predictions, compared with other calculation methods.

About the election strength criteria in calculations for long-term strength for non-isothermal processes of loading