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A simple and clear method of evaluating stress and strain ranges undernon-proportional multiaxial loading where principal directions of stress and strain arechanged during a cycle is needed for assessing multiaxial fatigue. This paper presents asimple method of determining the principal stress and strain ranges and the severity ofnon-proportional loading with defining the rotation angles of the maximum principalstress and strain in a three dimensional stress and strain space. This study alsodiscusses properties of multiaxial low cycle fatigue lives for various materials fatiguedunder non-proportional loadings and shows an applicability of a parameter proposedby author for multiaxial low cycle fatigue life evaluation.