In this paper, a model is developed to investigate the dynamic response of electromagnetic rail launcher rails subjected to a moving magnetic pressure. When the armature velocity reaches the critical velocity, destructive resonant regimes occur in the rails, significantly affecting launch accuracy and rail service life. The dynamic response of the rails is modeled using the Bernoulli–Euler beam theory, treating the rails as beams resting on an elastic foundation and subjected to a moving load. An analytical expression for critical velocity is derived using the characteristic equation method, and its accuracy is validated through finite element simulations implemented in ANSYS. Subsequently, simulation analyses are conducted to examine how varying design parameters influence rail dynamic response and critical velocity. The results demonstrate that critical velocity is dependent on rail geometric and material parameters, as well as the stiffness of the elastic foundation. The discrepancy between the analytical solution and simulation results presented in this study is within 5%. At relatively low launch velocities, the dynamic response of the rails remains minimally affected by the critical velocity. However, as launch velocity approaches critical velocity, rail deflection, shear force, and bending moment increase markedly compared to the static case, reaching maximum values precisely at critical velocity. Additionally, increasing the rail damping coefficient effectively attenuates dynamic responses, limits peak amplitudes, and alters the critical velocity of the system. Adjustments to geometric and material parameters of the rails result in variations in both critical velocity and the maximum deflection.