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The piston ring design using low tangential force to reduce friction loss has become a general trend in engine development - especially in passenger car engine - in recent years. This trend emphasizes the importance of stable sealing function that does not require much tangential force. Thus, it is important to grasp the correct pressure distribution between the ring and the cylinder. Reliable and accurate calculation to understand the pressure distribution has been an issue for many years among the engineers. In this report, we propose a new calculation method based on the piston ring contour in a free condition. Generally, the piston ring contour is calculated to achieve its correspondence to a given pressure distribution. By analyzing inversely, the pressure distribution is calculated when a ring contour is given. But as is well known, the solution is often unstable in inverse analyses. We introduced the idea of the method of least squares to avoid this problem.