In order to study the continuous collapse resistance of arc-frame structures, a refined numerical model of arc concrete beam-column substructures is established based on ANSYS/LS-DYNA. After reasonable verification through relevant tests, considering the changes of parameters such as arc beam curvature and beam section reinforcement, the quasi-static anti-continuous collapse analysis under the failure condition of the middle column is carried out. The results show that due to the influence of the initial curvature of the beam, the additional torque generated during loading will accelerate the failure of concrete and steel bar, resulting in the early failure of the arching mechanism and catenary mechanism of the structure. With the gradual increase of the curvature of the arc beam, the continuous collapse resistance of the beam-column substructure is gradually decreased, but the ultimate displacement is gradually increased. The arrangement of the beam waist reinforcement can effectively enhance the arch pressing effect of the arc concrete beam column structure, delay the decline rate of the resistance in the arch compression stage, and even appear the secondary increase of the resistance with small amplitude. When the top reinforcement of the end section of the side column beam breaks before the bottom reinforcement of the column section of the failed column and beam column does, the structure does not exhibit a significant catenary effect.