<p>This paper addresses the lack of proper design methods and the current status of being in the engineering imitation stage in the research of viscoelastic dampers for supporting helicopter tail drive shafting by proposing a systematic optimal design approach. First, a dynamic model of the tail drive shaft coupled with a viscoelastic damper is created using the finite element method. The influence of different viscoelastic dampers on the vibration characteristics of the tail drive shaft during the transcritical process and at supercritical stable speeds is studied, after which a test bench is constructed for verification. Next, the impact of the material and structural parameters of the viscoelastic dampers on the vibration characteristics of the tail drive shaft is investigated, and the parameters with the most significant impact are identified. Finally, a surrogate model is created using back-propagation (BP) neural network, with the key parameters of the viscoelastic damper as the input and the maximum displacement amplitude of the tail drive shaft during the transcritical process as well as the displacement amplitude at supercritical stable speeds as the output. Furthermore, the optimal design of the viscoelastic damper is conducted based on the NSGA-II genetic algorithm to minimize the displacement amplitude of the tail drive shaft. Test results show that the optimized viscoelastic damper achieves a 29.05% reduction in the maximum amplitude of the long shaft of the tail drive shaft during the transcritical process and a 20.84% reduction in amplitude at stable speed, compared with the viscoelastic damper before optimization. This study provides a complete methodology from modeling and parameter analysis to optimization design, offering theoretical and practical guidance for the vibration suppression design of helicopter tail drive shafts.</p>