Abstract: The two kinds of nonlinear buckling (primary buckling and secondary bifurcation buckling) of elastic arches are elaborated in detail. One kind of compact method of solving secondary bifurcation buckling is recommended, which is identified credible by examples. A full load-displacement equilibrium path is obtained by using the large deflection (displacement) finite element approach, in conjunction with arc-length method and Newton-Raphson iteration. The instability behavior of the arch with different rise-span ratios is investigated theoretically. Finally, a new kind of structure that is hybridized by arch and tensile cables is presented and analyzed in order to enhance its load-carrying capacity and to prevent the arch from the secondary bifurcation buckling. Some useful conclusions for the design of the arch are drawn.