We discuss a version of the mathematical theory of the quantitative description of the mechanical behavior of deformable bodies of different electrical conductivity and susceptibility to magnetization and polarization under the action of an external quasisteady electromagnetic field in both the radio and infrared frequency ranges.In various engineering processes in many areas of_ industry the thermal processing of devices m~de of bothtraditi, ,nal and newmaterials asing electromagnetiefields is receiving ever-wider application. For that reason, to establish reasonable regimes for such processing it is an important current problem to model the interconnection of fields of different physical nature in continuous systems subject to external electromagnetic fields. Certain results in this direction have been obtained for electrically conducting nonferromagnetic nonpolarized bodies in constant fields in the radio frequency range [17,19].In the present paper we study a version of the theory of quantitative description of the interconnection of electromagnetic, temperature, and mechanical fields in electrically conducting bodies that are susceptible to polarization and magnetization under external quasisteady fields of both radio and infrared frequency ranges. In constructing the models we used the properties of the physics of interaction of the field and the substance for such bodies and the methods of the thermomechanics ofpiecewise-homogeneous bodies [1,11, 12,15,18,20].We assume that the displacements and the strains and their velocities are so small that for the bodies being studied in the parameter ranges considered for electromagnetic action (H 0 < 107 A/m, where H o is the characteristic value of the external magnetic field intensity) the linear theory of elasticity is applicable, and that the effect of the motion of the medium on the characteristics of the electromagnetic field can be neglected We choose materials for which the mechanicoelectric and thermoelectric effects are insignificant. Thus we are assuming that the electromagnetic field is an external action on the body, whose effect on the processes of thermal conduction and strain is realized through heat emission and force factors (ponderomotor forces and moments). We state the initial relations for a quantitative description of the parameters of the electromagnetic, thermal, and mechanical processes in two stages [7, 12]. At the first stage we write the equations for the characteristics of the electromagnetic field in quasisteady approximation, and also expressions for the heat emission and force factors in terms of these characteristics. At the second stage we state the problem of thermomechanics for determining the parameters that characterize the thermostressed state.Consider an electrically conducting body subject to the action of an electromagnetic field. The field is created by a system of currents that traverse the exterior region (an inductor having time-modulated power) and are given by the expression j!~ (r, t) = ja(r, t) cos(cot +V 0), div f...