The KOBO extrusion is an unconventional elastic-plastic deformation process in which the phenomenon of changing a path of plastic deformation due to die cyclic oscillations by a given angle and with a given frequency is applied. As the results of the application of the oscillating rotary motion of the die, the reduction of the extrusion force is obtained. The numerical study of the KOBO extrusion of metallic materials is presented in this paper. The three-dimensional coupled Eulerian-Lagrangian (CEL) analysis is applied here. The relationship between the extrusion force and the punch displacement during the KOBO process was achieved. The effective plastic strain distribution in the butt was found. The results of the numerical computations are compared with the experimental data. The influence of the material hardening parameters on the cyclic loading phenomena (ratcheting, mean stress relaxation) in terms of the course of the KOBO extrusion was also examined. The proper determination of the material hardening parameters can help to optimize the KOBO process in terms of the reduction the extrusion force and the choice of the amount of die oscillations.