In the process of engineering use, the elastic coupling of the RT60 crane transmission system has a large noise and even breaks down sometimes. In this paper, RT60 crane transmission system is the research object. A finite element model and a discrete model for torsional vibration of transmission system are established by finite element method and lumped parameter method. Through the study of the finite element model and the vibration test of transmission system, the correctness of the system model, equivalent parameter, calculation method and MATLAB program are verified. Because of the high efficiency of the torsional vibration discrete system, the discrete model is used in this paper to replace the finite element model. The free vibration and response vibration of the crane transmission system are calculated and analyzed, and the reasons for the existence of the system noise are explained in the starting stage. Through the study of the vibration theory and the matching method of the elastic coupling, the CX-45-VFA-60-11 elastic coupling is proposed to replace the CX-45-VFA-11 elastic coupling. In this paper, the data signal is collected by the hall gear sensor, and the data are analyzed by the self-developed vibration tester. The vibration amplitude of the torsional vibration of the crane transmission system is greatly reduced by testing the transmission system of the replacement of the elastic coupling. This paper provides a theoretical guiding significance for the low noise design of the crane transmission system.