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Steel–concrete composite girder rigid frame bridges with V-shaped piers are a new type of bridge structure. Based on the traditional composite continuous beam bridge, part or all of the vertical piers are changed into V-shaped piers. This special structure makes them have the mechanical characteristics of both composite continuous beams and V-shaped piers. In this paper, the finite element model of the first steel–concrete composite continuous beam V-pier rigid frame bridge in China is established by simulation software, the construction process of the bridge is simulated, and the stress and deflection of the bridge in each construction stage are studied. At the same time, the stress of the completed bridge model considering the construction stage is compared with that of the completed bridge model without considering the construction stage. It is found that the stress difference between the two concrete slabs is as high as 2.7 MPa. The results show that the stress state of the bridge is greatly affected by the construction process. This study can provide guidance for the design and construction of such bridges, which is of great significance. [ABSTRACT FROM AUTHOR]