Simply the rectangle electromagnetic rail launcher’s rails and panel as double elastic foundation beam, and use the Dirac and Heaviside function to represent the distribution electromagnetic force caused by the moving armature and the concentrated loads on the rail respectively, then the dynamic response equation of the rail and panels in working condition was established in this paper. By the theory of modal orthogonality and regularization, the analytic solution of the rail and panels was calculated. Through an example, the rail and panels’ dynamic response was analyzed when the motion parameter and structural parameter were given, and the analytic solution’s reliability was verified through compared with the ANSYS numerical results. The research results in this paper give a foundation for rectangle electromagnetic rail launcher’s dynamic response analysis.