A formulation for elastic-plastic constitutive equations is given based on principles of continuum thermo-mechanics and thermodynamics. Energy dissipation and phase changes are included in the mathematical model. It is shown that kinematic hardening can be described properly for large deformations, by a two-fractions model. A mixed Eulerian-Lagrangian finite element method has been developed by which nodal point locations may be adapted independently of the material displacement. Numerical problems, due to large distortions of elements, as may occur in the case of an Updated Lagrangian method, can be avoided, movement of (free) surfaces can be taken into account by adapting nodal surface point locations in a way that they remain on the moving surface. Local and weighed global smoothing are introduced in order to avoid numerical instabilities. Applications are shown by simulations of an upsetting process, a wire drawing process and a steel quenching process. The results of the simulation of the upsetting process show satisfactory agreement with the results of an experiment carried out.