It is now well ascertained that a variety of instability modes can appear before the conventional plastic limit condition is met. In this paper, both flutter and divergence instability modes are investigated. First, the mechanical meaning of these instability modes is reviewed, and the criterion for detecting their occurrence is established. Based on an illustration example, the competition between the occurrences of each of these instability modes is analyzed, showing that the prevalence of a given mode is strongly related to both the loading conditions and the stiffness properties of the material system in hand.