Purpose <p>Belt conveyors are extensively utilized in various transmission applications. In the realm of mechanical modeling for a resilient supported conveyor belt, vibrational analysis of the multi-span axially moving beam system has attracted prominent attention.</p> Methods <p>This paper employs the complex transfer matrix method, which is tailored for multibody systems, to scrutinize the complex modal characteristics of a multi-span system equipped with multiple resilient supports and subjected to diverse boundary conditions. The complex transfer matrices of an axially moving beam and a spring-damping supporting element are derived. By leveraging the system’s topology, an overall transfer equation is formulated, enabling the analysis of vibrational features. To counteract the potential issue of ill-conditioning that may arise as the system’s span number increases, this study introduces a refined approach known as the reduced complex transfer matrix method. This method strategically partitions the complex state vector in accordance with the input boundary conditions of the system.</p> Results <p>Numerical simulation outcomes demonstrate the enhanced numerical stability of the proposed method. Moreover, this research delves into the potential factors that could influence the system’s vibration frequency, offering valuable insights.</p> Conclusion <p>The findings and methodologies presented in this paper are poised to serve as a robust and efficient tool, aiding engineers and designers in the optimal design and analysis of belt conveyor systems.</p>