Out?of?plane instability is one of the common instability forms of arc?shaped arched spanning pipelines. In this work, the ANSYS software was used to simulate the impact of wind and vertical distributed load on arc?shaped arch pipes under normal conditions. The influence of the arch foot displacement on the limit vertical distributed load is analyzed by finite element calculation. The analysis results show that the horizontal displacement of the arch foot has the greatest impact on the limiting vertical distributed load, which will rapidly decrease the displacement, the limiting vertical distributed load decreases linearly with the increase of wind load under the same horizontal arch foot displacement, and under different wind loads, the limiting arch plane displacement of the arch is concentrated within a certain range of the horizontal displacement of the arch toe, which can be used to monitor the arch tube deformation. Based on the above results, this work provides a certain reference basis for the design and safely operating of the crossing pipeline.