Slender structures with softening force-deflection characteristics are liable to exhibit snap-throughbuckling. This type of thoroughly nonlinear static behavior profoundly influences the situation in which the lateralloading is applied dynamically. In the case of harmonic loading the amplitude and frequencyof the force are the key parameters influencing snap-through. Although this is primarily a transient effect, the phenomenon of resonance may appear.Much of the previous research in this area is related to single-degree-of-freedom systems. Thecurrent presentation focuses attention on this type of behavior in very thin shallow arches from an experimental perspective, although a limited set of results from finite element analysisare included for verification purposes. For this kind of continuous system there is a surprisingly widevariety of possible behavior, e.g., the snap-through may occur in a symmetric or asymmetric type ofmode, various higher-order periodic response, a sensitive dependence on initial conditions, all of which occurabout and around potentially complicated equilibrium pathsand corresponding natural frequencies.The key results are associated with establishing appropriate definitions of snap-through as wellas delineating regions within parameter space where snap-through dynamics are likely to occur.The practical context for this work relates to the anticipation of sonic fatigue in thin curved panelstypically used as structural components in aircraft structures.