Abstract: The dynamic instability and chaotic behaviours of the well-known Mises Truss are investigated by computer simulation in this paper.The results show that periodic and aperiodic behaviours exist for certain values of the amplitude and frequency of the harmonic excitation.Dynamic loading in the form of a step function does not cause any chaotic response.This study reveals the importance of the chaotic dynamic analysis of structures in addition to their static and dynamic instability analyses.