Considering the non-conservatory force effect of cable and suspension bridge, the energy method is used to analyze the lateral stability problem of the downward bearing parallel double-ribbed oblique tension arch bridge, and the practical calculation expression of the transverse buckling critical load of the oblique tension arch bridge is obtained. The results show that the cable surface size, horizontal inclination angle, cable tension, anchoring position on the arch, the sagittal span ratio of the arch structure, the bending stiffness of the cross brace in the tangential surface of the arch, the number of cross braces and other factors have a great influence on the lateral stability performance of the structure, while the bending stiffness of the cross brace in the radial surface of the arch, the torsional stiffness of the arch ribs, and the vertical bending stiffness have little influence. After considering the non-conservatory force effect, the lateral stability performance of the structure is significantly improved by the cable.