A large number of technical and technological facilities work under the action of electromagnetic fields. In electroconductive bodies have significant largest electromagnetic forces that can cause movement or deformation of structural elements. The creation of effective methods of analysis of the distribution of the electromagnetic field and coupled nonstationary deformation of structural elements is topical at present time. The article contains a mathematical formulation of the problem of nonstationary deformation of structural elements under the action of electromagnetic fields. Coupling of electromagnetic field and mechanical field is carried out with the help of local electromagnetic forces. Further made the transition to a variational formulation on the basis of the task of finding the minimum of the total energy of the system, which includes the energy of the electromagnetic field. For the numerical solution the finite element method is used. Nodal unknowns in this case are the magnetic vector potential and displacements. The proposed method is applied to non-stationary deformation of the "inductor-billet" technological operation of magnetic-pulse processing of metals. Some results of the deformation are presented. A large number of technical and technological facilities work under the action of electromagnetic fields. In electroconductive bodies have significant largest electromagnetic forces that can cause movement or deformation of structural elements. The creation of effective methods of analysis of the distribution of the electromagnetic field and coupled nonstationary deformation of structural elements is topical at present time. The article contains a mathematical formulation of the problem of nonstationary deformation of structural elements under the action of electromagnetic fields. Coupling of electromagnetic field and mechanical field is carried out with the help of local electromagnetic forces. Further made the transition to a variational formulation on the basis of the task of finding the minimum of the total energy of the system, which includes the energy of the electromagnetic field. For the numerical solution the finite element method is used. Nodal unknowns in this case are the magnetic vector potential and displacements. The proposed method is applied to non-stationary deformation of the "inductor-billet" technological operation of magnetic-pulse processing of metals. Some results of the deformation are presented. A large number of technical and technological facilities work under the action of electromagnetic fields. In electroconductive bodies have significant largest electromagnetic forces that can cause movement or deformation of structural elements. The creation of effective methods of analysis of the distribution of the electromagnetic field and coupled nonstationary deformation of structural elements is topical at present time. The article contains a mathematical formulation of the problem of nonstationary deformation of structural elements under the action of electromagnetic fields. Coupling of electromagnetic field and mechanical field is carried out with the help of local electromagnetic forces. Further made the transition to a variational formulation on the basis of the task of finding the minimum of the total energy of the system, which includes the energy of the electromagnetic field. For the numerical solution the finite element method is used. Nodal unknowns in this case are the magnetic vector potential and displacements. The proposed method is applied to non-stationary deformation of the "inductor-billet" technological operation of magnetic-pulse processing of metals. Some results of the deformation are presented.