Following the rapid development of China's construction industry, the formwork support system has become one of the indispensable temporary facilities at construction sites such as industrial and civil construction, and bridges. This paper aims to study the progressive collapse (PC) resistance of the formwork support system with couplers under accidental loads. To this end, the software ANSYS/LS-DYNA was used to establish a finite element model, and the components were removed in a short time to simulate the sudden failure of local members under accidental loads. Besides, based on the growth rate of axial force, the authors compared the PC resistance of formwork support systems under the conditions of different failure time, failure positions, spacing of upright tubes, lift height of horizontal tubes, and semi-rigid node stiffness. The results show that: the shorter the local failure time of the structure, the more obvious the dynamic response of the remaining structure; under the failure of different members, the maximum growth rate of the axial force for the adjacent members ranked from large to small: angle member>side member>internal member; in case of the member failure, the maximum growth rate for the axial force in the adjacent members is proportional to the spacing between upright tubes and inversely proportional to the lift height of the horizontal tubes; with the increase of the node stiffness, the maximum growth rate of the axial force hardly changes, but the response time of structural yielding gradually increases. The research findings provide references for future research in this direction and the compilation of specifications.