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Electromagnetic launchers suffer a phenomenon referred to as armature transitioning: when the armature and rails suddenly lose contact with each other, damage can occur to the armature and the rails of the launcher. In this paper, we explore transient elastic waves as a possible explanation for the transitioning of solid armatures in electromagnetic launchers. We use a finite-element code to model the transient dynamics of a typical electromagnetic launcher guide rail. We found that dynamic rail deflections caused by the movement of the armature are similar in magnitude to those caused by the magnetic field, and that the contact pressure between the armature and the rails changes dramatically when the speed of the armature reaches the critical velocity of the rails.