In order to study the mechanical bearing behavior of arched sandwich roof structures, a full combination and independent action mode of concrete sandwich composite panels was constructed using the finite element method, and an arched steel–concrete composite sandwich roof with a span of 18 m was subjected to a numerical simulation test under a full-span vertical uniformly distributed load, with the bearing characteristics of the arched sandwich roof discussed in depth. The results show that the cross-sections of l/16 and l/2 of the elliptical arch sandwich roof are weak sections, and the tensile cracking of concrete appears for the first time in the upper and lower wythes of the elliptical arch sandwich roof, the von Mises stress level of the lower wythe of the l/16 section is higher under the ultimate load, and the roof shows four-part form failure characteristics. With the expansion of the cracking range of the upper and lower concrete wythes of the steel–concrete composite sandwich arch roof, the load–displacement curve of the roof structure does not decrease significantly, and the bearing capacity of the structure is high and the vertical deformation is small. The steel–concrete composite segment at the end of the roof effectively strengthens the edge constraint of the roof and improves the integrity of the sandwich roof. The upper and lower concrete wythes of the sandwich roof show a fully combined action mode in the elastic working stage and, when the concrete cracks, it shows a partial combined action mode.