In modern industry efficient electroheat technological processes are applied. This paper deals with such technological operations as induction heating and resistance welding of metals. In heated workpieces, coils, welded parts, electrodes the coupled processes of the alteration of the electromagnetic, thermal and elastic-plastic mechanical states take place. These complicated phenomena determine the course and definitive results of the technological operations. This paper describes numerical formulations, algorithms and PC-software developed for above-mentioned processes, as well as results obtained with this software. We developed the finite element axisymmetrical formulations for electromagnetic, thermal and static elastic-plastic mechanical problems. These formulations take into account thermal dependences of electric, thermal and mechanical material properties and non-linear magnetic properties of soft ferromagnetic steels. The Fourier's equation is solved by using the boundary conditions of the first, second and third kind. Besides, we take into consideration the thermal radiation in accordance with Stefan-Boltzmann's law. Solving elastic-plastic mechanical problem we use a special theory of plasticity with isotropic hardening. In order to solve three coupled problems (electromagnetic, thermal and mechanical) we developed and investigated numerical iterative algorithms taking into account the special features of the technological processes under consideration. A few technological problems of practical interest concerning induction heating and resistance welding of metal have been solved.