This monograph investigates the stability and vibrations of conductive, perfectly conductive and superconductive thin bodies in electromagnetic fields. It introduces the main principles and obtains basic equations and relations describing interconnected mechanical and electromagnetic processes in deformable electroconductive bodies placed in an external inhomogeneous magnetic field and under the influence of various types of force interactions. Basic equations and relations are addressed in the nonlinear formulation. A special emphasis is put on the mechanical interaction of superconducting thin bodies plates with magnetic field.