This book investigates the stability and vibrations of conductive, perfectly conductive and superconductive thin bodies in electromagnetic fields. It introduces the main principles and derives basic equations and relations describing interconnected mechanical and electromagnetic processes in deformable electro conductive 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 and special emphasis is placed on the mechanical interactions of superconducting thin-body plates with magnetic fields.