Abstract: Under the conditions such as cable failure, the failure modes of progressive collapse of cable-stayed arch-trusses are the buckling of compression members and tension yielding of tension members. To consider the buckling effect of compressed members, the current analysis generally adopts the method of dividing each member into multiple elements and applying initial geometric defects, which is inefficient and time-consuming. To solve this problem, based on the modified mixed hardening constitutive model of beam-column elements, combined with the nonlinear buckling material model of beam-column elements, a rapid analysis method for progressive collapse of cable-stayed arch-trusseses is proposed, and the correctness of the material model is verified by a calculation example. Using ANSYS/LS-DYNA to compile the subroutine of the proposed material model, based on the incremental dynamic analysis method, the progressive collapse analysis of a cable-stayed arch-truss under the cable failure condition is executed. On this basis, the incremental dynamic analysis of three kinds of reinforced structures is carried out, and the influence of reinforcing critical members on the resistance of progressive collapse under cable failure conditions is investigated. A study on progressive collapse fragility of cable-stayed arch-trusses is executed, and the resistance of progressive collapse is comprehensively evaluated. The results show that: the rapid analysis method shortens the calculation time by 39.89% compared with the traditional analysis method; after strengthening some mid-span upper chord and mid- span lower chord, the ultimate bearing capacity is increased by 16.67% at most, and the load values corresponding to the two forms are also improved. Based on the rapid analysis method, the resistance of progressive collapse of cable-stayed arch-trusses can be effectively evaluated.