The progressive collapse of a space grid structure which has a large number of members and a large span is the focus of current research. Before the progressive collapse of the structure, there is a problem of instability of the members. In this paper, dynamic nonlinear analysis of a super-long span latticed steel arch structure is carried out to study its progressive collapse process using a Kinematic Hardening Plasticity constitutive model compiled by Vumat material subprogram in Abaqus, which takes into account instability of the members. Differences in the dynamic response process of the structure at the collapse moment and the failure sequence of the members using the member stability model and the material failure constitutive model are compared. Compared with the material failure constitutive model, when the member stability constitutive model is used, the proportion of compressive buckling members in the structural failure is higher, and the bearing capacity of the structure is lower when the initial failure occurs. The structure suffers from localized member compressive failure rather than material yielding, which leads to the progressive collapse of the structure.