To understand the in-plane stability of a new type of double-box open-spandrel circular steel arch, the in-plane elastic buckling and elastic-plastic stable bearing capacity of the steel arch were investigated by theoretical deduction combined with finite element numerical simulation, the influence of shear force on the failure modes of arch section was analyzed, and the design method for the in-plane stable bearing capacity of the steel arch was proposed. First, according to the distribution of shear force on the arch section, the influence of shear deformation of double-box open-spandrel circular steel arch and local shear deformation of chord web on the in-plane elastic buckling was studied. The formula of pure compressive elastic buckling load of double-box open-spandrel circular steel arch was derived considering double shear. Then, based on the design principle of axially compressed column of steel structure, stability coefficient and regularized slenderness ratio were introduced to draw the stability curves under pure pressure. Finally, the stable bearing capacity design formulas of the integral failure mode of double-box open-spandrel circular steel arch under several common load conditions were analyzed. The arch structure analyzed in this paper is novel, and the calculated results of the proposed elastic buckling load formula were in good agreement with the finite element analysis results. At the same time, the binomial formula of axial force and bending moment was used to check the overall stable bearing capacity. The results can be used as a reference for future scientific research and practical engineering design, which has important practical significance.