Abstract This paper presents the nonlinear inelastic time-history analysis of truss structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on an updated Lagrangian formulation, while the material nonlinearity is captured by tracing an empirical stress–strain relationship in the elastoplastic range. The presented truss model is capable of capturing several failure modes of member such as buckling, yielding, inelastic post-buckling, unloading, and reloading. An incremental-iterative solution scheme based on the Newmark method and the Newton–Raphson method is adopted for solving the nonlinear equations of motion. A computer program is developed to predict the nonlinear inelastic responses of truss structures. Numerical examples are presented to demonstrate the capabilities of the proposed program in capturing the nonlinear responses of space truss structures under earthquake loadings.