Leakages of bolted pipe flange connections of water-containing hydrofluoric acid pipelines were frequently reported by the extraction section in the fluorine chemical industry. Water-containing hydrofluoric acid can cause severe injuries to human beings due to its strong causticity. The water-containing hydrofluoric acid pipe was a short lined pipe, so a lot of flange connections and supports were adopted in the pipeline. In this paper, the finite element models of the pipeline were established to analyze the internal force of the pipeline under conditions including internal pressure, temperature, self-weight, and so on. Based on this, the equivalent design pressure of the flange connections was determined. The results of the stress analyses of the pipeline showed that leakages were mainly caused by a large bending moment, due to the unreasonable layout of the piping supports under self-weight. When the pipeline was supported on the beam of the pipe gallery, which is not necessarily beneficial to reduce the bending moment of the pipeline, and the flange connection was close to the supporting beam at the same time, leakages frequently occurred in this flange connection. To support the pipeline reasonably, the flange connection should be placed at zero bending moment positions. Therefore, the positions with zero bending moments of the pipeline with equal and unequal spacing supports were obtained under gravity load, to provide a basis for the rational support of lining piping.