Of interest here is the influence of loading rate on the stability of structures where inertia is taken into account, with particular attention to the comparison between static and dynamic buckling. This work shows the importance of studying stability via perturbations of the initial conditions, since a finite velocity governs the propagation of disturbances. The method of modal analysis that determines the fastest growing wavelength, currently used in the literature to analyze dynamic stability problems, is meaningful only for cases where the velocity of the perfect structure is significantly lower than the associated wave propagation speeds. As a model structure to illustrate this point we select an elastic ring subjected to external hydrostatic pressure which is applied at different rates epsilon (appropriately non-dimensionalized with respect to elastic axial wave speed). The ring's stability is studied by following the evolution of a localized small perturbation. It is shown that for small values of the applied loading rate, the structure fails through a global mode, while for large values of the applied loading rate the structure fails by a localized mode of deformation. An analytically obtained localization time t(1) is found to be a very good estimate of the onset of instability time at high loading rates