Progressive collapses are resisted by the catenary mechanism in reinforced concrete (RC) frame structures undergoing large deformations. Research to date has mainly focused on the nonlinear dynamic progressive collapse resistance demand of this type of structures under the beam mechanism (that is, for small deformations), and that the catenary mechanism is lacking. As a first attempt, this study establishes a dynamic amplification factor for evaluating the resistance demands of RC frames under the catenary mechanism. To achieve this, an energy-based, theoretical framework is proposed for calculating the aforementioned demands. Based on this framework, the analytical solution for the collapse resistance demands of regular RC frames under the catenary mechanism is readily obtained. Numerical validation indicates that the proposed equations can accurately describe the progressive collapse demand of RC frames undergoing large deformations.