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With consideration of the importance (for oil passing and blow-by) of the issue of three-dimensional deformation of piston rings in a cylinder due to either installation stress, or operational gas, friction, and thermal loads the subject of piston ring distortions still generates continuing interest. The current paper demonstrates application of a mathematical model developed in the former works of the authors for analysis of the distortions of arbitrary cross-section rings loaded by tangential force. Applications of the model to the several typical cross-sections are given for illustration. The work is a necessary step for the development of a comprehensive three-dimensional theory of piston ring installation and operational distortions.