Based on the geometric equations,physical equations,kinetic equations,and electrodynamics equations of thin shell,the thermal-magnetic-elastic coupling equations for a current-carrying cylindrical shell are established. Using the linearization method,the linear iterative equations on the thermal-magnetic-elastic problem are obtained and transformed into normal Cauchy type including eight basic unknown functions. The temperature field in the cylindrical shell and integral eigenvalues of the temperature field are derived after considering Joule‘s heat effect in an electromagnetic field and introducing the thermal equilibrium equation and generalized Ohm’s law. The results that the stresses,temperatures,and deformations in the current-carrying cantilever cylindrical shell change with variation of the electromagnetic parameters are discussed. It is proved that the stresses,strains,and temperatures in plates and shells can be controlled by changing the electromagnetic and mechanical parameters by considering a specific example.