Abstract: To perform efficient dynamic computation of a tensegrity structure and to consider local dynamic buckling of the flexible bars during large overall motions of the structure, the reduced-order dynamic model of a slender bar under compression is proposed in this research. The model is a five-node discrete one with lumped parameters of axial stiffnesses, torsional stiffnesses and lumped masses that are achieved by the equivalent analysis of the static and dynamic characteristics of the continuous bar. First, the expressions of the axial and torsional stiffnesses are deduced by the equivalent analysis of the static behaviors such that the discrete model can predict accurately the pre-buckling and buckling of the bar and approximate its post-buckling. Second, the expressions of the lumped masses are deduced by the equivalent analysis of the kinetic energy such that the linear motion of the bar can be accurately described. Third, the distributed parameters of the torsional stiffnesses and lumped massed are determined by the equivalent analysis of the natural modes of transverse vibration. The appropriate combination of their values can largely reduce the relative errors of the first two natural frequencies up to less than 1%. Fourth, the transient dynamics equations of tensegrity structures are established in the frame of global coordinates, and the method of static condensation is used to enhance the computational efficiency of the iterative solution. Last, the simulation and experimental tests are carried out and the results are compared for the quasi-static compression, modal analysis and impact dynamics of a spherical tensegrity structure. The effectiveness of the proposed reduced-order dynamic model is verified for modeling statics, natural vibration and transient dynamics of tensegrity structures. And the influence of the variation of structural parameters on the mechanics of tensegrity structures is analyzed. The proposed modeling and computation method is expected to be applied for dynamic analysis and control of complex tensegrity systems, such as planetary probes with soft landing, large-scale deployable space structures and lattice materials.