The purpose of this study is to investigate the static and dynamic stability of an elastic truss model. The truss model· is subjected, separately, to static loads, dynamic step loads, and dynamic impulse loads. For each loading, the results are presented in the form of stability boundaries and displacement criteria. For the static loading, the stable equilibrium displacement fields are determined by minimizing the energy of the model. The type of failure, limit or bifurcation, and the critical load magnitudes, are determined based on plots of load-frequency curves. For the dynamic loadings, the magnitudes of the critical load are based on the criterion presented by Budiansky and Roth. The stability boundaries for the static loading and the dynamic step loading are compared. It is found that the static critical load values are three to seven times the magnitude of the dynamic step critical loads. It is found that the truss model shows a local and global failure for a certain class of loading. The magnitudes of the critical loads for local instability are significantly less than the magnitudes of the critical loads for global instability when the loading is symmetric or near symmetric. It is found that the critical load magnitudes for a symmetric loading are much larger than for an asymmetric loading. Constant displacement curves (based on displacement constraints for the truss model) are also presented. These results are helpful in indicating loading configurations to which the response of the truss model is sensitive. / M.S.