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Here are shown on stress and vibration evaluations and application of piping system in petrochemical plant with an actual example. While stress evaluation by thermal growth has no argument on the calculated results, vibrational evaluations have some different results in accordance with the evaluation methods. In case of the static stress evaluation, the ASME B31.3 code defines 7000 cycles of fatigue life in operating the piping system with a design condition. However, the method of vibrational evaluation on piping systems in petrochemical plants has not been established clearly, yet. In this study, it is purposed to present the requirement of a vibrational evaluation method for petrochemical plant piping systems, with an actual application.