The objective of this study is to analyse the dynamic stable and unstable behaviours of a space truss using an accurate solution obtained by the high-order Taylor method. Because numerical solutions can lead to incorrect analyses in the case of a space truss model due to the being parameters large, we analyse the solution’s behaviour using essentially an analytical solution obtained by the multi-step high-order Taylor method. In detail, the dynamic instability and buckling characteristics of the SDOF model under step, sinusoidal and beating excitations are investigated.