<p>A new methodology is proposed for assessing the fatigue strength of structural elements in beam and plate forms with coatings under variable high-frequency loads. It is noted that, due to technological residual stresses in the base and coating after the composite formation process, the composite’s stresses require additional clarification. For preliminary assessment of the possible strength of a plate specimen under biaxial cyclic bending, an analytical limit state criterion is proposed. The criterion allows the determination of the predicted probable location of crack formation in the specimen due to material fatigue. Additionally, the criterion is distinguished by the absence of undefined quantities in its composition. Methods for experimental-computational determination of residual stresses in beam and circular plate specimens are presented. For the analytical criterion of the limit state, it was verified using experimental data for a circular plate based on VT1-0 titanium alloy and coated with TiN using vacuum plasma deposition. For a circular plate with a thin-film titanium nitride coating under biaxial bending, experimental data on the fatigue resistance of the material were obtained and compared with data calculated based on the analytical limit state criterion. At a₂/a₁ values of 0.66 and 0.94, the differences between the experimental and calculated values of the endurance limit in equivalent stresses were 3 and 1.3%, respectively. This, in turn, allows one to assert that the presented analytical limit-state criterion enables a quite accurate assessment of endurance limits under the considered type of stress state, with only endurance values under simple uniaxial loading available. Simultaneously, it is shown that the calculation method for the endurance of the considered materials with coatings also allows determining the coating’s influence on the corresponding endurance characteristics without conducting experimental tests.</p>