In this study, we shall investigate the dynamic instability behavior of Zetlin-type cable domes, which are well-known among the cable dome structures that the lightweight hybrid structure using compression and tension element continuously. The structural behaviour of the cable dome shows a strong nonlinearity according to the initial stress and external forces. Therefore, we determine the shape by applying initial stress abd then investigate the indirect buckling mechanism by the dynamic external force. Also, we investigate the generation of chaos in the indirect buckling, which the dynamic nonlinear problem is reacting sensitively by the initial imperfection.