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The paper demonstrates a possibility to assess endurance (high-cycle fatigue) of a structural element allowing for its geometry, material properties, and type of loading. An analytical relation is derived, where the parameters representing the endurance of a structural element are given in combination (i.e., in the form of dimensionless quantities) rather than individually. The proposed method is implemented numerically and the results obtained are compared to some available published data.Introduction. One of the most critical tasks a design engineer faces is to assess endurance (high-cycle fatigue) of a structure at the design stage. The available methods of solving this problem, which were developed based on the physical [1], statistical [2], and phenomenological [3] approaches, fail to provide a possibility to allow for an element's geometry, material properties, fabrication techniques, and type of loading over a wide range of their variation. The present work involves the well-known method of dimensional analysis [4]. It enables us to consider the parameters, which have an effect on an element's endurance, not individually but in combinations, by arranging these parameters in dimensionless sets (complexes π i ). Based on these complexes, an analytical relation (hereinafter, the relation) is derived to assess endurance of a structural element.Results and Discussion. For the purpose of deriving the above-mentioned relation, we selected the parameters in view of the known physical concepts of endurance of structural elements (in this case, of metal materials) under cyclic loading. The number of the parameters chosen can have an influence on the endurance assessment accuracy. To derive the relation, we consider the bending and tension-compression fatigue test results for standard [5] and nonstandard specimens. The last-mentioned ones have some of their geometrical parameters deviating from the standard requirements [5].Since the tests were carried out in the cyclic loading mode, we have added the parameters involved in the differential equation for vibration of a bar [6]: stiffness EI (where E is the material's elastic modulus and I is the moment of inertia of the element's cross-section at the maximum stress location), material specific weight γ ρ = g