The flare system is an indispensable safety facility in petrochemical production. The function of the flare system is to collect the tail gas emitted from the production of each device into the main pipe of the flare, lead it pass through the liquid separation tank and the water seal tank in turn, and finally to the high-altitude flare for combustion and discharge into the atmosphere. The high temperature of flare gas pipeline will cause the pipeline to expand under heat. Due to the large thermal stress caused by the thermal expansion of the pipeline, the load on the nozzle of the connected equipment will be increased, which is easy to cause safety accidents. Taking the flare system of a whole factory as an example, this paper introduced a simple discriminated method to measure the flexibility of the pipeline system. The software CAESAR II was used to establish the model of the main flare pipe and the liquid separation tank in the whole factory. The calculated stress state of the pipe system meets the requirements of ASMEB31.3, and the stress of the liquid separation tank nozzle meets the technical conditions of the manufacturer. It is hoped that this method can provide some reference for the regular inspection of pipelines.