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A model is developed to investigate the dynamic response of an electromagnetic railgun, induced by a moving magnetic pressure during launch of projectiles. As the projectile velocity approaches a critical value, resonance can occur and cause high amplitude stress and strain in the rail at the instant and location of the projectile's passage. In this study, governing equations of a railgun under dynamic loading conditions are derived that illustrate a lower-bound critical velocity in terms of material properties, geometry, and barrel cross section; this represents the worst case or a lower bound solution for the structure under a dynamic loading condition. A study is then performed to show the effect of these parameters on the critical velocity of the barrel. Accordingly, the model that accounts for projectile velocity and gun construction can be used to guide and improve barrel design.