Abstract: The out-of-plane secondary bifurcation buckling load-displacement equilibrium paths of an elastic-plastic arch are traced by a high-efficient tracing strategy. The elastic-plastic out-of-plane secondary bifurcation buckling load under a concentrated load at the top of the arch and a full-span distributed load are obtained, which are compared with that under in-plane ones. The calculation results show that: for elasto-plastic arches with the same section and without an out-of-plane brace, the in-plane secondary bifurcation buckling load is less than that of out-of-plane one under a concentrated load and it will occur before out-of-plane buckling; The out-of-plane secondary bifurcation load of the arch with a 0.2 rise-span ratio is the biggest. The out-of-plane secondary bifurcation buckling will occur before in-plane buckling when the arch is under a full-span distributed load and the out-of-plane secondary bifurcation load of the arch with a 0.3 rise-span ratio is the biggest. When the rise-span ratio is 0.1, the difference between in-plane and out-of-plane secondary buckling loads is biggest. For elasto-plastic arches with the out-of-plane brace at the arch apex, the effect of the brace on bifurcation buckling load is not obvious under a concentrated load and only the buckling modality is changed. However, the brace may improve the out-of-plane buckling load significantly under a full span load especially for the arch with small rise-span ratios. The out-of-plane secondary bifurcation buckling will occur before in-plane one.