Abstract: The finite particle method is a technique used in structural dynamics analysis based on the Newtonian mechanics. This study focuses on developing a method to calculate the equivalent stiffness of moving particles and improving the expression of Rayleigh damping within the finite particle method framework. To validate the accuracy of the proposed damping force calculation formula, a case study was conducted involving the free vibration of a cantilever beam structure. Moreover, this paper investigated how various structural parameters affect the natural frequencies of an unfolded truss structure. Transient dynamic analysis was also performed on a large flexible space truss structure. The results indicate that the finite particle method can effectively consider the nonlinear properties of cables and analyze the nonlinear stiffness characteristics of structures. A cable-stayed structure and a concentrated mass at the end significantly impact the structure’s natural frequency. Although the attenuation of truss structure vibration primarily relies on its stiffness and structural damping, depending solely on structural damping may prolong the time needed to restore the structure to a stable state. The results also demonstrate the stability of the Rayleigh damping of the finite particle method proposed in this paper in dynamic problems and its applicability to nonlinear dynamic analysis of large flexible space truss.