This study aimed to examine the dynamic response of large converters to the braking process. Based on the rigid-flexible coupling theory of the multi-body dynamics, and by adopting the finite element method and multi-body dynamics software Recurdyn, this work constructed a variety of rigid-flexible coupling dynamic models of converter transmission systems. With torsional vibration of the converter furnace during braking as the object of analysis, this research studied the pattern of the impact of speed change of driving motors, braking time, and rotational damping of the system on the torsional vibration characteristics of converters during the braking process. Comparison of the simulation results indicated that the rigid-flexible coupling mode had a greater impact on the simulation results and simulation efficiency. In particular, the analysis model using elastic units in the coupling between rigid and flexible bodies could effectively simulate the torsional and vibrational response of the converter braking process. Dynamic simulation results showed that increasing the braking time and rotational damping of the driving motor could effectively reduce the torsional vibration of the furnace under certain conditions. Within the same braking time, the maximum value and the continuity of the driving motor acceleration had the greatest impact on the torsional vibration amplitude of the furnace, and optimal control of furnace torsional vibration could be achieved when the acceleration was a second-order curve.