Based on the cusp catastrophe theory

the lateral buckling of parallel dual-arch-ribs was studied. The displacement function

as well as the energy representation were constructed when there was a lateral buckling in the dual arch-ribs. By mathematical transform，the energy cusp catastrophe model was established

then the system's equilibrium surface M equation and bifurcation point set B equation were obtained. Through the analysis of buckling conditions of dual-arch-ribs system

bifurcation point was calculated

and the formula of lateral buckling critical load was derived，furthermore

a new calculation method of lateral buckling critical load of parallel dual-arch-ribs was proposed. At last

comparing theoretical results based on the cusp catastrophe theory with those obtained from FEM

it is verified that the calculation method presented is sufficiently accurate. The study has opened up a new way for the lateral buckling of the arch structures.