The article presents the results of research on the effect of the change in coordinates that determine the location of the common vertex of the parabolas and ellipses demonstrating the asymmetric shape of the rings sliding surfaces on the change in the thickness of oil film, the amount of scraped oil, and the oil left on the cylinder wall, once a set of selected sealing rings has passed, as well as the results concerning friction losses. Mathematical relationships of the asymmetric shapes of the rings sliding surfaces were presented, and the values of coefficients characterizing selected parameters of oil film and friction losses were determined. It was confirmed that there is a large dependence of the coordinate values of the vertices determining the asymmetric shapes of these surfaces on the condition and cooperation between piston rings and the cylinder bearing surface, and mainly on the amount of the oil scraped in the selected engine strokes.