Numerical simulations of the KOBO extrusion process are presented in this paper. The coupled thermomechanical Eulerian-Lagrangian approach was applied for the three-dimensional finite element model. The dynamic explicit Euler forward method was used in numerical calculations. The elastic-plastic Chaboche model assuming isotropic and kinematic hardening under variable temperature conditions was applied to describe the behaviour of the material under cyclic loading. In numerical computations Chaboche material model implemented in commercial software, as well as the proprietary one written as FORTRAN procedure were tested. The numerical results present the stress and strain distributions in the extruded material, as well as an increase of temperature due to the plastic work and friction. The shape of plastic strain zones was verified experimentally. The approach presented in the paper is a promising numerical tool to simulate the KOBO process.