For the single-track railway concrete-filled steel tube tied-arch bridge, since restrictions of the bridge width will inevitably lead to a relatively smaller ratio of width to span using long span.The stability is a very prominent issue in design and construction. Taking a 136m span through concrete filled steel tube tied-arch bridge as an object, considering the influence of geometric and material nonlinearity of arch rib, its space stability analysis of the whole bridge is made using finite element program. Its stability factor and the instabil-ity mode are given under the most unfavourable load condition. Instability of the structure is mainly shown in out-plane instability of arch rib. Elastic buckling factor is greater than the general requirement, which satisfies the requirement of the bridge elastic stability. The effect of geometric nonlinearity on stability of the bridge is smaller while the effect of material nonlinearity is greater, which should be considered in the stability analysis of long span arch bridge. After the arch ribs are progressively loaded, the ultimate loads of the arch ribs are obtained. Effects and variation law of transverse brace layout, arch rib inclination angle and ratio of height to span of the arch to the stability of this bridge are revealed.